Will disconnecting and reconnecting the positive battery cable while engine is running cause gauges to fail?

There could be a few different issues that could cause the temperature gauge on your 2008 Ford Focus to read hot when the engine is not actually overheating. Here are a few things to consider:

Failed thermostat: The thermostat is responsible for regulating the flow of coolant through the engine. If the thermostat is stuck in the closed position, it could cause the temperature gauge to read hot even though the engine is not overheating.

Failed temperature sensor: The temperature sensor sends a signal to the temperature gauge to indicate the engine's temperature. If the temperature sensor is faulty, it could cause the temperature gauge to read hot even though the engine is not overheating.

Wiring issue: If there is a problem with the wiring that connects the temperature sensor to the temperature gauge, it could cause the gauge to read hot even though the engine is not overheating.

To determine the cause of the issue, it may be necessary to perform some diagnostic tests and possibly replace some components. A mechanic or a professional auto repair shop will be able to diagnose the problem and recommend the appropriate repairs. It's also a good idea to keep an eye on the engine temperature and take note of any other symptoms or issues you may be experiencing. This information can help the mechanic diagnose the problem more accurately

Remove the gauge cluster and check for a bad ground. If it is bad you can resolder the trace on the back of the cluster back to the groung pin for the connector.

You may try this.

Here's the throttle body relearn procedure

Clear the PCM adaptive memory
1) Disconnect the negative battery terminal.
2) Run a jumper wire from the positive battery cable to the now disconnected negative battery cable terminal. NOTE. Do this with the negative cable DISCONNECTED from the battery. The short circuit you're creating here is designed to drain all power from the capacitors inside the PCM. Leave the jumper connected for about 2-mins.
3) Reconnect the negative battery cable to the battery.
Turn off all electrical accessories before proceeding. Turn off headlights, blower motor, radio, wipers, etc.
4) Turn the key to run and wait for all warning lights to turn off. During the period the PCM will command the throttle body plate to sweep from full open to full close to "learn" the new positions.
5) Start the engine and let it idle for a full 10-mins until it reaches full operating temperature. During this period the idle may be higher than normal. It should slowly drop as the engine heats up. Watch the engine temp gauge and note when it reaches operating temp. Then continue to let it idle for an additional 5 minutes. It will continue to adjust idle during this period.
6) Drive the vehicle at various speed so the PCM learns shift points.

Replacing a fuel pump has nothing to do with instrument cluster lights or the clock staying on. Unless you shorted wires , did you disconnect the negative battery cable before hand ?
The body control module (BCM) performs the following functions:
• A/C compressor request
• A/C cooling fan
• Exterior and interior lighting control
- Daytime running lights (DRL)
- Automatic lighting control
- Fog lamps
- Interior lighting
• Battery rundown
• Chime
• Gauge control
• Instrument cluster indicator control
• Fuel gauge control
• Temperature gauge control
• Theft deterrent
Interpreting all of the driver warnings sent by the control modules on the class 2 serial data line
Sending the information to the instrument cluster in the form of a SPI serial data bus message
The following list of messages are sent by the BCM to the instrument cluster:
• Fuel gauge position
• Temperature gauge position
• Oil pressure
• Low engine coolant
• Check oil
• Volts
• ABS
• High beam
• Low fuel
• High temperature
• Washer fluid level low
• CRUISE
• BRAKE
• SERVICE VEHICLE SOON
• Door ajar
• Seat belt
• THEFT SYSTEM
• PRNDL
Check the fuel level sensor wires , the fuel level sensor is a input to the BCM .

I suggest you take it to a ASE certified repair shop an have it diagnosed .

Depends on year model, GM had definite issues with Instrument Clusters, but if the engine is actually hot, and what you are telling me is true it sounds like a faulty thermostat, but more than likely you have an instrument cluster issue. Take to someone with a Tech 2 Diagnostic and have it diag'd properly

The most likely cause is due to the radiator fan constantly running and the engine not getting to operating temperature, thats why your temp gauge isnt going up, check all related wiring to the cooling fan and make sure there no bare wires that could be causing a short to ground causing the fan to constantly run, secondly check the fan relay, if all of that checks out check the coolant temperature sensor because the information from that sensor tells the computer when to turn the fan on and off, if the sensor is bad it could be telling the computer the engine is hot when in fact its not.

cooling fan has a relay. check it first. Then check the ECT, Engine Coolant Temperature Sensor. It is on the engine and sends a signal to the PCM, Engine Computer.
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Section 03-03: Engine Cooling 1996 Aspire Workshop Manual
DESCRIPTION AND OPERATION Cooling Fan, Electric WARNING: WHEN WORKING IN THE ENGINE COMPARTMENT, STAY CLEAR OF THE FAN BLADE. BECAUSE IT IS ELECTRIC AND TEMPERATURE SENSITIVE, IT CAN START AT ANY TIME IF THE IGNITION IS ON.
The electric cooling fan is an electro-drive type. Its operation depends upon engine temperature and ignition switch (11572) position. If engine coolant temperature reaches 97°C (207° F) and the ignition switch is in the ON position, the engine coolant temperature sensor (ECT sensor) (12A648) sends a signal to the powertrain control module (PCM) (12A650) which turns the engine cooling fan motor (8K621) and fan blade assembly on. Because it cannot operate unless the ignition switch is ON, the engine cooling fan motor and fan blade assembly does not operate after engine shutdown. The fan control relay (FC relay) is located in the LH front corner of the engine compartment, between the battery (10655) and the headlamp assembly. Circuit protection is provided by a 30A fuse labeled COOLING FAN in the main fuse junction panel to the left of the battery. If the vehicle is equipped with air conditioning, an additional relay is installed in the circuit. The A/C clutch control relay (19D572) bypasses the engine temperature portion of the circuit. The bypass circuit allows the engine cooling fan motor to operate whenever the A/C switch is engaged.
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Fuel pump/sender access is through cover under rear seat.


Fuel Gauge

1. Remove the instrument cluster. Refer to the procedure in this section.
   

1. Using a jumper, connect the battery positive terminal to the fuel gauge "+" terminal and the battery negative terminal to the fuel gauge "-" terminal.
   

1. Connect one lead of a Rotunda Instrument Gauge System Tester 014-R1063 or equivalent to the "F-U" terminal of the fuel gauge (9280), and connect the other lead to the "-" terminal of the fuel gauge.
   

1. Adjust the instrument gauge system tester to the resistances shown in the illustration.
   
   
   
   
   

1. If the fuel gauge does not operate as specified, replace the fuel gauge. If the fuel gauge is OK, return to the Pinpoint Test.
   

Fuel Level Sensor

1. Remove the fuel level sensor (9275). Refer to Section 10-01 for the removal procedure.
   
2. Measure the resistance between terminal A and terminal B of the fuel level sensor.
   
   Connector Shown From Component Side

1. Adjust the fuel tank float to the following positions:

1. If the resistances are not as specified, replace the fuel level sensor. If the fuel level sensor is OK, return to the Pinpoint Test.
   

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My solution to dashboard instrument panel gauges and lights not working was to disconnect negative cable to car battery, then reconnect. After doing so, everything worked.

And the solution to instrument panel coming on and off sporadically may also be a loose battery connection.

From 2005 H2 Lover

Try removing the battery cables so the computer will be reset. Leave it off for about 15 minutes. Then reconnect it. The computer will reset to the default settings. Every time the battery is removed and stays disconnected for 15 minutes or more, it will reset itself.