automatic thermostat control for heater circuit

I have an idea for a stupidly over complicated filament dryer that would need to use a space heater or something similar to heat a donut shaped chamber that would have filament on one side and desiccant on the other and a heater circulating the air at a higher temperature to dry the filament and I have no idea how to have variable control over a space heater or if arduino is even the best solution. My original idea was to use a variac or something similar but that gets expensive quick. is there a way to do this in a cost effective way?

$20 hair dryer.