Pop the hood and take off the lid to your overflow tank and see if the tank is dry, meaning the rad is low. So only fill the overflow tanks and wait much longer (if you don't have a plastic see through overflow tank) - as you have a mystery car, no year, make, model,mileage... Out of 10,000,000 vehicles yours does not stand out.
[stuff people who are looking at it see and people on YA are idiots because they can't see. and you won't tell them. Some actually design cars.]
Because my FIRST GUESS IS THAT YOU DO NOT HAVE ANY COOLANT. Usually the reason for overheating. Probably blew a rad hose so all the coolant is on the road somewhere.
Easiest way to fix is take off the caps and refill and fix the leak. Cost to you is the cost of coolant and checking to see if a coolant hose blew or let go or the water pump is leaking.
Thermostats have been made for over 100 years...so they got the bugs out...they don't fail.
97F out? Does not impress me much. Engine runs at 180F so WAY HOTTER. Anything less is called cool.
5 minute drive more won't hurt it Just don't touch anything. They will work on it when it cools. So tomorrow morning it will be done.