Wont start when hot

I assume from the question that the engine is cranking over but will not start. Hence there is no issue with the starter motor on a very cold start.

At 40 degrees F you are getting closer to freezing. When this happens again I would check the operation of the fuel pump.
Take the fuel cap off the fuel tank and have someone switch the ignition on and off a few times. (just the ignition - don't start the engine up). Turn it on for 10 seconds or so and then off. If you listen at the fuel filler opening with the cap off you will be able to hear if the fuel pump starts and stops. If it is working it should start and then stop a few seconds later each time you switch on the ignition because the computer shuts it down in a few seconds if the engine is not started.

If the fuel pump is operating I would be looking for some electrical gremlins. You would need to check that the fuel injectors are getting power and that the spark plugs are also.

Ideally you would need to a quality scan tool connected to the car when you have this very cold no start condition whilst trying to start the car to see what faults may be present because it should pick up some malfunction if the start problem goes away when the temp rises a few degrees over 40F.

If by "won't start" you mean that the STARTER struggles to turn, I suspect that the starter motor is having a temperature-related failure.
Replace the starter AND solenoid, and inspect the starter wires to verify that they're not burned or corroded. If the wires going to the starter, or their terminal ends, look in any way dicey, replace them too.

The air from the heater core will be as hot as the coolant temperature of the engine. 80 Degrees is the opening temperature of the thermostat and that will be where it remains until the engine starts to work or the ambient temperature rises.
Thermostats come in a couple of different opening temperatures so check around for one that opens around 85 degrees if you want hotter air in the cab
Another point is to close the recirculating vent door to the cabin as the heater core is trying to heat fresh freezing air if it is open

check electronic spark unit ie coil pack going open circuit when hot
will run but when turned off will stay open circuit untill cools down then closed circuit then will wprk fine

The engines run very lean for fuel efficiency. Although a "cold start sequence" gives the impression of freezing temperatures, the operating range is much higher. The water temperature sensor (some have 2) may be staying too warm for the reset. You may need to change the sensor. Then the fuel mix will be richer and the engine will start.

First thing to do is replace you fuel filter, If there is a check engine light have the code read, Most parts store will do this for free. Get the code number type that into google for further advise.

It seems strange that you have this starting/no power issues when it over 70 degrees outside but not when it is cold. When it is cold the battery and starter are normally under more pressure to start the engine and it is also harder to burn and atomize fuel when it is cold.
The reason I suggest removing the trim panel and checking voltage at the ignition switch is that is the best place to start. The ignition witch has to have power present at the switch and must distribute that power as the key is turned to operate accessories and the starter motor when turned to the start position.
Flag This

possibly the coolant temperature sensor is faulty

sound like coolant temperature sensor is open or not working.scan it to see when engine get operating temperature when coolant temperature get 190 degrees the coolant temp sensor should show 190 degrees if it shows 80 degrees or lower it not working replace it.the coolant sensor control coolant fan.when it gets hot it resistance changes or lower.the pcm grounds it .then cooling fans will run.

Change air temp switch.