No. the 2000 series ULAs have a max running temp of 125 deg C, fact not opinion,and a test conducted by one retro computer components supplier saw the chip running at half that temperature so no heat sink required, the rest of the chips run even cooler.
Like the car engine that red lines at 5000 rpm running it at half that speed is unlikely to cause any nightmares.
Things such as removing/fitting peripherals whilst powered up or said peripheral failing and taking out the ULA is the main killer, you will not find any one offering a provable example of heat killing the ULA in the 40 odd years of its existence.
Fitting the switching reg as you have done is the biggest favour you have done to the computer re cooling, also fitting a CMOS version of the CPU knocks power requirements down quite considerably.
The zeddy is not as fragile as you may think so don't overthink it too much, just use it and enjoy it.
