Normal? No.
It's best to keep your CPU below 80C and if you see temps above 80C, it's time to start worrying since Intel CPU at 90C will start thermal throttle to keep CPU running. At 100C, PC should automatically shut down to prevent CPU burning up. If it doesn't, you'll burn your CPU. Max what Intel CPU can withstand short-term is about 105C.
Did you had CPU thermal issues before or did they began after your service?
If it's the latter then my best guess is that the thermal paste you used to replace old thermal paste has worse thermal throughput than the stock thermal paste had.
Here, i'd open the laptop and replace the thermal paste with liquid metal since liquid metal has the highest thermal throughput. Though, be very careful when applying it since it's electrically conductive and if it ends on anywhere else than CPU die, it can (and most likely will) short circuit your PC.
Another thing to do would be placing your laptop on the table or even on a stand where the intake/exhaust fans have more clearance. Putting laptop on the bed is one of the main factors why it overheats (since intake/exhaust vents on the bottom side will get blocked by cloth).
Btw, what specific issue you had that got fixed when you updated the BIOS?