back to the actual topic of this thread..........
If I understand what you are saying, you have a heating pad, without any type of controller hooked up to it, (thermostat, dimmer, etc.) and you have a strip thermometer that is most likely placed above the substrate, which is reading around 80 degrees?
If that is correct than the hot side of your tank is way too hot. You should be reading about 85 degrees directly above the mat, on the glass, under the bedding. (As mentioned above by Bitsy).
The problem with only getting one (either the thermometer or the thermostat) is that you need the one to use the other properly. If, for instance, you get the thermostat w/o having a proper thermometer, you won't know how hot/cold your thermostat is set. If you get a thermometer w/o a thermostat, you will simply know that your heat pad is too hot and won't be able to do anything about it....
If what I said above is correct about your heating situation what I would recommend doing in the mean time is to either:
(1) get a thermostat first, and try to use your strip thermometer to set the thermostat by taking it off the glass, then putting it directly on the bottom of the tank and getting a temporary reading that way.
OR
(2) get the thermometer first, then put something on the glass, on the bottom of the tank, to kind of buffer the effect of the heat mat. Maybe taping some newspaper or something similar down there so that it makes it impossible for your snake to borrow and have direct contact with the heat mat.
Just some suggestions, if I was in this situation that's what I might do. I'm sure other members on here will have other suggestions. Good luck!