Nooo! The whole point of having a cybernetic arm/hand is that you can just stick your hand in a great big beaker full of liquid nitrogen-cooled eyeballs and not have to worry about getting frostbite!
You can also just grab the hot pan from the oven and not have to worry about getting burned.
You want temperature sensing? Put a thermistor in one of the fingers and a little OLED display on the arm (or even better: in a HUD that can only been seen in the user's eye). A nice, high temp one 👍