I have a Hampton Bay Windward II ceiling fan with remote control.
Unless the room temperature is 80 degrees or above, neither the fan nor the light will operate. If I leave the main power in the on position, and the remote control is set to off, the fan will turn on all by itself once the temperature passes the 80 degree point. Once this happens, it cannot be controlled with the remote. To stop the fan, I need to turn off the main power. Then with the fan stopped and the power off, I can use the remote to set the fan speed and/or activate the light, after which I restore power and then I can use the remote. If I should turn off the fan using the remote, then I have to perform the same off-on process all over again.
However this will only work if the temperature is above 80 degrees. If the temperature is 79 degrees or below, the fan and light will not work at all.
I have put fresh batteries in the remote and checked the dip switches on the remote as well as the fan itself, but nothing seems to work.
Any suggestions?

Definitely sounds like a problem with the remote. You can contact Hampton Bay for a replacement, or bring the whole fan back to Home Depot and exchange it under warranty.

The fan has a feature where it can switch on and off by temperature, but it should affect the light.