I don't see the temperature of my GPU in Task Manager, and neither do I see the temperature of my CPU. To see either one, you need to have hardware and/or software that measures or, more likely, estimates the temperature.
CrystallDiskInfo is a good example of (free, lightweight) software that, in the absence of hardware, estimates temperatures. An example of hardware is a chip added to motherboards or their fans that estimates the temperature based on fan speeds.
In either case, an estimate is sufficiently accurate, because the goal is to determine whether the CPU or the GPU is running hot, not to gauge its exact temperature. More accurate hardware is certainly available to testing labs.
I agree with you that an indicator in Task Manager of CPU and GPU temperature would be a great idea. A summary of S.M.A.R.T. status would be good, too.
P.S. This is a user-to-user community forum. No one from Microsoft here.
If you wouldn't mind my asking about your cooling system:
1- How much noise does it make?
2- Can you dispense with the case fans entirely?