Without a IR temp gun how are you measuring the basking spot? In a 20gal and a 100 watt bulb I bet the hotspot being created under the lamp is over 100F.
For your set up you don't have to have a tstat and instead can use a dimmer to dial in the 100 watt bulb to the power you need.
http://www.amazon.com/gp/product/B00...=sr_1_3&sr=8-3 (Lowes, HomeDepot, WalMart, and Target will have these too.)
You can also use two 60w bulbs and have one on each side, or whatever watt bulb you need to create the correct temps. If you keep the entire tank in the 80-85F range your snake will be fine. There are plenty of keepers that do not provide their collection with a hotspot and their collections are thriving with nothing more than a good ambient temp.
Without a tstat on the uth you need to UNPLUG it now. Having it unregulated is placing your snake in great risk. Google images of burned snakes and you will see what I mean.
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