So,you say temperature increment in seconds is not matter.Do you think paralleling to 2 7805 can effect to heating.?
You need to quantify somewhat your temperature otherwise we cannot understand what you are trying to say.
If the 7805 is just warm to the touch is OK but not hot.
Your original 7805 may be faulty, so you need to replace with a new one. And do watch the orientation when you put the new one back in.
I think is just plain wrong diagnosis of the problems you are having. Instead of just hypothetical about seconds and rise, do the measurement. Please measure the voltage when you do write back.
Pin 1 to Pin 2 is about 9vdc.
Pin 3 to Pin 2 is 5vdc.
Otherwise, don't expect the sensor to last forever.
Edit: The designer don't even bother to put a heatsink to the 7805. So don't even think of paralleling 2 7805. It's not the problem!
Edit: to avoid language barrier, I attached a picture to differentiate sensor and 7805.