Take JJ's advice and use 4-lo. I've four-wheeling way up in the rockies and w/ steep hill climbs for miles and never had a problem when using four-low and the correct gear. Even, my friends tacoma had it's light come on when we where up there because he wasn't using four-low.
Without 4-low you are making the torque converter slip alot to keep engine RPMs up to generate enough power to move. However, all that slipping generates alot of heat. Lower gearing elinimates the problem, so slip it into 4-low.
However, you are running in a climate that frequently gets well past 100F (50c = 122F). Honestly at those temperatures you probably want to look additional cooling. Most vehicle have trouble at those temperatures. Just driving across the southern california deserts you see water stations every couple miles and signs telling you to stop and let your car cool.
An additional tranny cooler might be a good idea. You can get a decent one for 50 dollars and easy enough for a do it yourselfer to install.
Check the link below for some populare ones. I'd go with the 16,000 or 19,000 one. The other are 1.5" and a little too thick to squezze in. I was planning on installing one this summer
http://www.jegs.com/webapp/wcs/stores/s ... ryId=17689
Nice write up on the install
http://www.ws6transam.org/transcooler.html
Finally, I wouldn't keep driving and pushing it. What the light means is the tranny fluid has reached about 275F or 135C which is quite hot for the fluid. I wouldn't run it like that for any length of time. You very well could damage something if you keep on it. If it does happen, the owners manual suggests stopping and revving the engine in park or neutral to the light goes away. That way you are circulating fluid through the transmission and cooler without putting any load on the tranny.