The car is a 1999 Mercury Sable: the car fan blows but the heat does not get hot when turned on and takes forever to get lukewarm

You need to have the fluid changed and replaced with fresh fluid. The reason it is currently boiling the fluid and causing it to spill out is because of the drop in viscosity of the current fluid and is unable to perform its duties. I would take it to a local AAMCO transmission shop, they have always done good work for me.

If no blower is running check for a bad fuse for the heater blower or a bad blower motor and or resistor or burned connector to the blower motor

plugged heat exchanger is both heater hoses hot valve under hood closed

i have a 99 ram 1500. i change the blower motor and thermostat. and it still blows lukewarm. how can i fix the problem.

see if you can turn the fan by hand with the car not running. if so chek the temp switch. unplug it and start car fan should start rite away. if not chek fuses.

The clicking noise is the motor for the "blend door". The heater core and the air conditioning side share the same ducting. When you move the knob a small motor moves the door letting the respective hot or cool flow happen.
The heater core is probably blocked. The engineers at Ford have the coolant hoses bypassing the core with a WYE at the firewall. The coolant takes the path of least resistance and stops FLUSHING the heater core and it eventually clogs.

do you see a leak anywhere on the ground under the car??
check the oil and make sure it is not mixing oil and water

does it blow out white smoke?  If so it might be a head gasket issue.  I know mercury sables were infamous for head gaskets.

The blend door that regulates the airflow over the heater core may be stuck in the AC position. It is inside the case and is most difficult to get to. There may be a YouTube video that may help you locate it and test it.

you have a broken or stuck temp blend door in the heater case. or the servo motor is broken. this sits on top of the heater case