1996 ford contour gets hot , no hot heater or temp guage movement

Do you smell coolant inside of the vehicle. If so then chances are your heater core is going.

Well it could be a problem with the fan relay, or it could be a safety feature of the computer.
if the computer finds a problem with the cooling fan or the engine temp sensor, it will turn on the fan to try to prevent overheating. Even if the engine is cold.
If the check engine light is not staying on, I would check the fan relay for power and ground.

It is much more likely you are low on coolant or you have an air bubble trapped in the cooling system. You should bleed the cooling system to get any trapped air out and make sure it is full of coolant.

it is the upper sensor that sends coolant temp to your computer. check that sensor first.

Sounds like you have an air;lock in your cooling system.Try placing a bleeder on the return hose to the heater core ........looks like a small tap

is the temp gauge going to hot? if so, it may be going into failsafe mode where it shuts off half the cylinders to protect the engine.

check your engine coolant temp sensor. It sends a signal to tunrn the cooling fan on.
Does the cooling fan come under the hood?
Does the cooling fan come on when you turn the a/c on?

report back.

You may have an air pocket in your system which some times happens.  One way to get rid of it is to take the upper hose off on the engine side,  fill your system with water until it runs out from your engine block, replace the hose, start your car turn you heater on and set to hi keep the radiator cap loose until the temp start to rise then close tight.  Once the air pocket had been remover you can drain some of the water from the radiator using the lower drain plug and add antifreeze.   

If fan doesn't work period, check fuse for blower fan, if fuse is good, check fan relay switch.

dear sir,

the solution to your problem is simple. yes you say that it has a new water pump, but the reason that a vehicle bubbles out of the expansion tank is because the water pump is not circulating coolant, the coolant boils in the engine and bubbles out of the expansion tank. secondly the reason the fan never kicks in is because the temp sensor is not seeing the heated coolant because the water pump is not circulating the coolant through the cooling system. 3rd. the heater never gets hot because the water pump is not circulating coolant through the heater core in order for it to get hot and provide heat. and the temperature gauge never seems to go up because yup you guessed it, the water pump isnt circulating coolant in order for the engine temperature sensor to see hot coolant and thus send a signal to the engine temperature gauge as to the coolant temperature. i know you said it has a new water pump, but i have heard that this type of vehicle may come with a plastic fin pump. i would remove the pump and check the passages for foreign matter{ trash} in the passages as well as the condition of the new pump. also one last thing, the reason the vehicle died on the road in the first place was probably because it overheated. happy hunting and please post to see what you found. i am a mechanic by proffession.

actually the contour and mystique both have this problem they tend to overheat and ruin engines and transmissions when the fan quits working the best fix is a kit you get from ford or advance auto parts it makes the coolong fan run all the time the engine is on and this will save you lots of problems in the future, not only am i a master automotive tech but i have owned 6 of these cars. the 96 mystique beng my favorite. mercury version. good luck james