Your hot side is not getting over 82ºF ? The question I have is what kind of pad are you using. There are HUGE differences between brands and wattages some are designed not to get overly hot and may not be able to cope with a PVC cage insulation value and a cool room.

A RHP (RADIANT HEAT... Where the idea that a radiant heat source is actually a Convection heat source is baffling to me) does not change air temps in my experience with two (one test set up for 5 months) the best air temp change I managed was 4º. They (RHPs) replace UTH not ambient air heating methods. Personally I find a standard fluorescent tube mounted inside the enclosure lifts the ambient air temps exceptionally well. It is safe as its maxed temp (100ºF) is below a contact burn point and it is unlikely to lay against a light top mounted long enough to become unable to digest food. I find a 2 foot tube lifts 10º over the room temp. They are also about the cheapest convection heater around. (radiation aka RHP produce electromagnetic waves that transfer heat to objects, not air, just like the sun. Conduction transfers heat to objects in direct contact like a UTH or stove. Convection is a heat source that heat the air directly and causes thermal air currents like a wood stove or CHE.)

Temps ideally are Warm (hot) side surface 90ºF (88-94ºF)
cool side surface 80ºF (78-84ºF)
Ambient air temps 79-81ºF (75º-85ºF)

I quoted the temps that are closest to universally accepted the bracketed figures represent the extremes max and mins I have seen from reputable sources. It depends a bit on snake size too small snakes generate more heat while digesting than big snakes do so lower temp warm side temps are sometimes used (88ºF is common) with sub adult snakes.