I have a 2 story house with a basement. The bathroom on the top floor directly over the garage only gets warm water. It is the furthest bathroom from the gas water heater located in the basement. Is there anything I can do to fix this problem?

If you turn on just the hot water will it eventually get up to full temp? If not, your mixing valve is likely partially plugged on the hot side. Back to you.

If you turn on just the hot water will it eventually get up to full temp? If not, your mixing valve is likely partially plugged on the hot side. Back to you.It will eventually get to full temperature but by that time your shower has to be short or you will run out of hot water.

Have you considered installing a hot water circulating system to the farthest bathroom branch?

Have you considered installing a hot water circulating system to the farthest bathroom branch?
I have not checked into that. Is this something that installs directly on the hot water tank or is it more involved. I am in no way a plumber so I hope my question is not dumb.

I think something is still amiss. Once the hot water finally reaches your shower you should still have 40 gallons of hot coming up from the tank. Could be wrong but I think its worth you time to disassemble the cartridge and clean the ports. While the cartrdige is out place a towel over the valve body and turn the main on for just a moment to cl;ear the lines.