How can I warm up/cook food while cycling?
I don't think it would be convenient or practical to use any kind of stove or hotplate while you are actually riding. If you are carrying a backpack or have things on a rack a propane backpacking stove can be very fast for creating a hot meal on a break.

To cook/warm while you are actually riding I think your best bet would be to use a Flameless Ration Heater like you find included in many military-style Meals Ready to Eat (MREs). I think you would still want to assemble the FRH and MRE into a packet and attach them to a rack while you ride because the packaging can get pretty warm.