I have a problem with my 2001 lincoln ls v8, my car heater, I've already changed the thermostat and water pump. When I drive it hot, I came home and antifreeze boils in the reservoir and empties

Air in the system ! Cooling fans not coming on ! You put the thermostat in right ? What engine ? 3.0 or 3.9 L ,Hook up a scanner that can view sensor data parameters , what is the PCM seeing from the cylinder head temp sensor .
I would think air pocket in the heater core because no heat coming . Heater hoses going into the fire wall , are both hot ? Hot water valve working ?
How to Fix Car with No Heat Easy

Thermostat is stuck. Not sure about the added antifreeze, but might be good idea to flush system while changing thermostat.

radiator is probably stopped up and when you allow coolant into the heater core which is a small radiator itself. it get sufficient releive to run normal. or your sender for the temp guage is bad and the car never is really overheating.

The heater control valve restricts hot coolant from flowing thru the heater core when the air cond is running.
Usually if it fails, you have no heat.

Does the engine temperature also take that long to get to operating temp (around 200 F)? If it does, your thermostat may be on its way out. Check your coolant level first.

have you ever checked whether the radiator is blogged? or the water pump does circulate the water? or even check whether the matrix is not blogged.

charge the ac system and if it doesnt leak and the ac works right you should be good, if not you need to change the pump.

Water pumps go bad when they leak. If there is a lack of circulation, there could be a clog in the system. Is the heater core getting hot on both tubes at the firewall? If not, then the heater core is clogged up. Has anyone ever put too much sealant into the cooling system that would cause an overheat condition due to lack of circulation of coolant?

Good luck on this repair.

Check the 'heater control valve,' which is attached to the heater hose line under the hood. If it is malfunctioning, it will prevent hot coolant from reaching the heater core, with the result being no heat. This is a $30 part, usually not too tough to get at, although I've never changed one on a Lincoln.

you probably have air trapped in the system. Have dealer or radiator shop bleed system.

I assume your cooling fan is working.

what engine v6 or v8?

SECTION 303-03: Engine Cooling 2001 Lincoln LS Workshop Manual
DESCRIPTION AND OPERATION Engine Cooling The cooling system components include the:

• block heater (optional)
• cylinder head temperature sensor
• fan blade, fan motor and fan shroud assembly
• radiator
• pressure relief cap
• degas bottle
• radiator draincock
• water pump
• oil cooler (optional)
• water thermostat

The water thermostat:

• controls the engine coolant temperature.
• allows quicker engine warm-up.

The degas bottle:

• provides a location for system fill.
• contains coolant expansion and system pressurization.
• provides air separation during operation.
• replenishes the engine coolant to the system.

The fan blade draws air through the radiator to help cool the engine coolant.
The fan motor:

• operates only when the engine is running.
• will not operate when the engine is off.

The engine coolant flows:

• from the lower radiator hose to the water pump.
• from the water pump to the engine block and the cylinder heads.

A closed water thermostat returns the engine coolant to the water pump. An open water thermostat allows the engine coolant to flow to the radiator.
Unsatisfactory coolant materials:

• Alcohol-type antifreeze does not provide adequate water pump lubrication.
  • has lower boiling point
  • reduced antifreeze protection
• Alkaline brine solutions will cause serious engine cooling system damage.

The cylinder head temperature sensor provides a signal to the temperature gauge.

• will invoke failsafe cooling.

The optional block heater:

• electrical heating element is installed in the block cooling jacket.
  • uses a standard 110V (220V in Europe) electrical supply
• keeps the engine coolant warm during cold weather.

The auxiliary water pump (3.9L only):

• provides heater coolant flow boost.
• has a secondary function of providing engine-off cooling.