The important thing is the temperature inside the cage. This can vary from the room or outside temperature either way.
Try to provide a temperature on one end in the mid 70s and on the other end in the low to mid 80s.
I do prefer under tank heating, but a ceramic bulb is adequate as well as long as it maintains the needed temperature.
As far as feeding it during winter it's an either or situation, not a reduction of food. You either cool him for 8 weeks or so and don't feed him at all, or you keep him at normal temperatures and feed him normally.
Unless you are planning on attempting to breed him there is no requirement that he be cooled, so you can just keep everything the same through the winter.
A word on the thermostat you placed a link to. For that money you can order a ZooMed Repti Temp 500R, a model which I use in many applications and prefer greatly over the ESU model.
The best price I have found online is at Reptile Direct.
http://www.reptiledirect.com/product...23&1=301&3=112