Tires DO heat up on loaded up touring bikes. Especially if temps are high. Mexico gets pretty warm. Lots to consider here:
Where are you from? Canada? If you come from a cold climate with only a 4 month riding season then perhaps your tires never heat up? Do you often feel your tires to monitor their heat? I do ... and am continually amazed just how HOT they can get after high speed, spirited riding.
A few other considerations:
How heavy are YOU and all your luggage? Passenger on board? All this matters. The KLR is not designed to carry massive weight and it's small tires can heat up if overloaded.
For a heavy load maybe add a few extra PSI? On your KLR you'd want to go from Kawi's recommended pressure (I'm guessing between 25 to 29 ? PSI (rear). Go up 3 or 4 PSI. Less increase for front.
Heavy Duty tubes cause MORE HEAT in your tire on the highway. Heavy tubes are good off road and resist punctures better but cause tire to run a bit hotter ... and thus tire will wear out more quickly. Trade off. If you don't ride Off Road, then use Heavy Duty tubes but NOT Ultra HD tubes.
Type of tire?
A more OFF ROAD biased tire may get hotter than a more road biased tire.
A cheap, Chinese import 50/50 also can get hotter than say a steel belted Metzeler Tourance or Michelin Anakee.
Most Llanteros (tire shop guys) in Mexico are pretty good getting the tire to fully seat. If it's way out of alignment then that too can get it hotter than normal. Get it lined up and balanced (close is good enough for a KLR).
Good luck. Don't worry too much unless something is RUBBING on your tire. If you smell burning rubber ... well, that would be your clue!