What does a beginner need to know to build a programmable heater based on resistance heating?
Actually, a beginner doesn't need to know much at all. You can buy the control system off the shelf.



This is an Industrial Temperature Controller. You simply connect up the temperature sensor, an solid state relay (they often come with both of these). Let it run through its learning cycle. Then you program in the temperature you want, and watch it automatically control your deep fat to the temperature you want.

They're available for very little money on eBay. They solid state relay it comes with is good for 10A (2.5kW heater).