I think you're off by about 90 orders of magnitude for the actual heat death

Our nearest star, Sol, will grow cold well before then.

But even that is estimated to take trillions of years after it runs out of hydrogen for fusion.

Err, no. You're well out there! By literally 10^100 years or more https://www.youtube.com/watch?v=uD4izuDMUQA

Healthy adults don't think about this. It's rational but it's too rational and it makes you unable to function. If you find yourself fixed on the inevitability of the death of everything, maybe seek counseling.