Ok...finally got the relay I'll use to control the heat. I'm doing some testing using a transistor and 5V off of the RPI to power the coil. I'll post the circuit as soon as I finish testing.

As you can see my testing rig is fairly sophisticated :-) I also figured out a number of optimizations related to the display of the graphics, and have re-written the UI. With a few weeks of testing, I've had accurate and quick responses when using the touch screen.