If the tub is not getting hot water the issue is probably with the hot water heater. The hot water heater may have tripped a breaker or the pilot light went out.

If it is an electric hot water tank, you more than likely have a burnt out element

Hot water pipe rust first as compared to the cold water pipe for the same chemical composition of the water.

If shut off the hot water valve then you take off your supply line from your hot water valve to your faucet and then turn your hot water valve on slowly (with of course a bucket or something to collect the water under it) and if you can see you have water pressure and flow then most likely the problem would be in your faucet on the hot side. If you have no pressure or flow when you turn the hot valve on then it could be debris plugging your hot water pipe or your hot water service valve (angle stop, straight stop) which older galvanized pipes are known to do so. To fix the problem you would need to find out where the problem is then either fix or replace the faucet or replace the angle/straight stop or try back flushing the hot water pipe and or replace the pipe with pex or copper pipe.

If hot water burned down houses there would be many more fires.