Best heating & Cooling suggestions

Let me start by saying Roxie is our 1st snake ever. In the past we had this set up for frogs. It sat empty for roughly 10 months. Since the environment was established more like a terrarium we tweaked it when we put her in it to be more suitable for a snake. She seems comfortable and did eat yesterday but I noticed this morning that the hotter portion of her tank was at 77⁰ it was at 81⁰ yesterday. The light bar has a 24 hour setting so that is what we had it set at. We also have a warming mat (taped to the bottom left corner wall).

I guess my question is should we get different light for the tank?

We live in Western NY and it is currently about 68⁰ in our house at 7 am

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