what i would do, is run it under cold water.
Hot water runs faster than cold water because the molecules in hot water makes it go faster than cold water.
The water pipes are full of cold water. All that cold water has to be flushed from the pipes before the hot water from the tank reaches your faucet.
Maybe u have a plubing problem
Either the cold water froze or someone shut the cold water riser to the upstairs floor.
You probably have a blocked or frozen pipe into the H/W tank.
Technically it won't matter as the hot water is made from incoming cold water. However it would be cheaper to turn on the cold water and let it run very slowly, more than a drip. If you leave the hot open, the heater will be turning on and off all night.
Same reason hot water gets hotter when run longer
they have to run cold water over their arm.
You could install a recirculating pump near your hot water tank and run a pipe from the furthest fixture that has hot water to this pump. This pump would then circulate the hot water back into the COLD inlet of the hot water tank and have hot water available at each fixture when you want. You would require a check valve where the recirculated water enters the cold supply to your hot water tank. CALL A PLUMBER THAT HAS FREE ESTIMATES!!!