Help with my thermostat?

[Lefitte]

I'm new to keeping snakes, but after a lot of research, I took the plunge and brought home my little aberrant California kingsnake a little over two weeks ago. I seem to be doing things right as far as I can tell but I'm having some issues with the thermostat. Here are some details:

Glass 20x10x7.5" tank with locking/sliding screen lid
Newspaper substrate, layers plus shredding
Small ZooMed heating pad on one side of the tank attached to Zilla on/off thermostat
Digital thermometer [bought a week ago, analog before that] with probe touching the hot side
Two hides, one cool one hot, mopani branch, and water dish
Approx. 2 month old Cal king, approx 16" long named Eir

So, being new to this, I knew I needed a thermostat but ran into a wall when trying to figure out how to get the probe in the cage. Since the directions say not to attach the probe to the heating pad directly, I have it taped underneath the tank, beside the heating pad. We've had the a/c running pretty much nonstop with this recent heat wave but our house rarely goes under 80. Our air vents are on the floor and there is one a few feet away from her tank so I've blocked off the air flow from getting under the tank on that side.

The digital thermometer has been reading 84-95, which doesn't make me happy, considering the swings in temperatures, but I noticed once again that the temperature has gone over 100. This time it was 101, last time it was 105 when I caught it. I'm considering looking into proportional thermostats but if the problem has to do with the a/c air circulating then it may not help as much.

Any idea for how I can fix this issue? The last thing I want is for her to get accidentally burned by the heating pad not shutting off due to a thermostat. I mean, that's why I have one in the first place. Before you ask, I don't have any better place to put her tank. That's the only spot safe enough with enough room, outlets, natural lighting, ect for her to stay. Any help or ideas would be greatly appreciated!