If you want that much simplicity as you don't seem to have a good grasp of the electronics the simplest thing I can think of is using a simple autotransformer.
2KVA 0-130VAC VARIABLE TRANSFORMER-MPJA, Inc. as an example.
That one's rated at 2000va which means 2000 watts, you could probably look around and find one cheaper that's rated to a more sane value, I dont' think you'd need more than about 500va or so (va = watts) The biggest problem would be designing your heating coil so that it could deliver that much power.
You would need a temperature probe in the beaker and then you just turn the knob till you get the temperature you want, it would be a little tricky to get it to actually hold the temperature automatically.