Here is a prior similar question and response that might help -
I would take the access cover plate off the heater to SEE if the main burner is firing, not count on listening - sometimes a couple of screws holding it in, usually just settles into place with a couple of "ears" slipping into place to hold it in.
Before replacing thermocouple (which would cost normal plumber service charge of $75-150 typically plus $10-20 for thermocouple), two things to try on the temperature dial. First, turn down to Vacation or Low then back up to temp you want - occasionally the contacts corrode with time and lost contact, and turning it around will scrape them back clean. If that does not work, try turning your thermostat to Low or Vacation, then back up 10-20 degrees higher than desired temp and see if it kicks on. As thermostats get old they sometimes "drift" - lose accuracy. Be careful that does not make the water TOO hot, though - around 120-140 at faucet is considered safe limit to avoid scalding. Consumer Product Safety Commission says 120 (especially for disabled or elderly with slow response times or loss of feeling, and small children), OSHA says 140, most manufacturers and "old-school" rule of thumb 130.
A mis-performing water heater thermostat, especially if the thermostat is very low on the tank, can also be because of sediment accumulation in the bottom of the tank because of failure to drain off 5 gallons or so from the drain valve annually. What happens is if it is partly (or completely) immersed in sediment, the surrounding sediment acts as an insulator and heats up quickly during firing of the heater, so reaches indicated temperature long before the water reaches that temp - leading to warm but not fully hot water.
Also on thermocouple - take flashlight and make sure it is well into the pilot flame - the tip and about 1/2 the length of the brass end of the thermocouple should be immersed in the pilot flame - rarely the "fingers" or twist-knob that tightens the thermocouple in place will slip and let it drop down to the flame is not heating the thermocouple enough. At times, it can be getting enough heat to let the pilot gas flow, but not enough to open the gas control valve for the main burner.
One other thermocouple issue - make sure (after turning gas valve to PILOT and removing cover plate) that the thermocouple is not buried in rust - that can affect the temperature that it sees and cause it to not work correctly. If it is, get plumber to service it or for DIY turn off as entirely (valve control to off), let cool completely, then carefully (without breaking off pilot or gas fittings) brush or vacuum (easier) the burner element and pilot area clean. Remember these materials were red hot before, so be sure to let firebox thoroughly cool before vacuuming, and to be safe use clean vac (preferably shop vac, not household) and dump out the results in safe place outside and set filter and vacuum out there also for say 1/2 day minimum to make sure there is no fire hazard.
In summary - if water gets warm and reheats after use (though not to full temp) probably a thermostat issue (drift, sediment, or whatever) because it is firing but just not getting to full temp. If not firing and reheating at all, then thermocouple or rarely the gas control valve is the problem.