I even took the phone out of the case, and still getting cool-down warnings. Looks like its time for a trip to Verizon, a required update shouldn't trash my phone.
Galaxy S5
Take it into Verizon and let them do a factory reset and reload of your information. You will need to give the device 3 to 5 days after the reset for the phone to settle down to normal again. This should handle most if not all of your problems. Wish you the best,