More than likely this is an issue with the cruise control vacuum pump. Within this system this is the only component that would be affected by heat. So, I suspect you have a leak in the line going from the pump to the servo.
So, we should connect the pump to a gauge and then drive the vehicle to find out if the pump is working.
Here is a guide that talks a little bit about this:
https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge
The other likely cause is the servo itself.
I am attaching the info on how to replace this below so let me know what questions you have.
Thanks
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Monday, January 31st, 2022 AT 11:22 AM