Don't get a flat! Just finished a much longer than necessary ride home in 108F.

I got 2 today. the same one repeated when my patch didn't stick due to the heat. the first time i got a huge blister on my thumb due to the heat of the rim and tire and force needed to get the gatorskin back onto the rim.
obviously if you do get a flat, walk to the nearest shade.

Helly, you mentioned headaches. are you getting enough water at other times of the day? Drinking plenty of fluids off the bike ensures that you have an adequate reserve for on the bike as it is possible to lose more than you can absorb back through your stomach (in the same time frame). I've found headaches come from dehydration and overexertion before the body has adapted to the heat.

Take it slower than normal. especially as your body adapts to the riding temperatures. today was one of the first days of the year I've ridden at 108. I was riding a good 4-6mph slower than I normally do. ---these are on flats. hills will also have a decrease -- don't beat yourself up about it. Your body will let you know when you can push again. and then, slowly build up. push yourself in the morning, if you're worried about losing fitness.

I've experienced minor heat exhaustion(?) several times. once was more then just minor. some things i've learned to look for in my body:

-excessive sweating or not as much sweating. pay attention to yourself, with riding the bike, we have a self generated fan which can evaporate sweat. depending on your humidity levels and personal sweatiness you can figure out what is normal. as it gets hotter, there will be more sweat. slow down and do major climbs, more sweat.
-Sudden change in sweat levels. this goes hand in hand with the above. but if you notice you're drenching the ground and 15 minutes later, your skin is bone dry. stop, get off the bike and into shade, and chilled water! i've never had this happen on the bike, but I know if i have no more sweat, I've now in heat stroke territory. Unless i never got sweaty, I better be sweating!
My question if I notice my arms dry up, am i sweating anywhere? (my face, upper lip is the last to go i think) If I am, then i know I'm still 'ok'. i still need to stop, get out of the sun, get something cold and take a breather, cool off, and take it easier when i get back on the road.
-chills. If it's hot out and a breeze hits you and you chill - this is a major warning sign. a cool breeze feels lovely on sweat, but if you feel cold, warning sign activated. i have to cut my effort, and immediately start chugging water - cold if possible. if not cold, find a gas station and get cold. The next step for me after chills is to begin to stop sweating, so getting to where I'm still sweaty but not cold is a good idea.
-goosebumps. no chills here, just goosebumps on the arms or legs. the skin may be dry or not. for me, a sign of insufficient electrolytes.
-headache. If i've let it go this far, bad girl... for me headaches are a sign of dehydration. if i am moderately active, and do not do any major increases of water intake, I found it took 3 days to induce dizziness and vertigo(it happened once and never again!). being more active and in the heat, I could imagine it would be a matter of hours before i got to that level of dehydration.

those are my warning signs. My fixes have been simple: I slow down, increase fluids(chilled prefered), make sure that i'm getting plenty of electrolytes. and take advantage of shade for any stops. (an AC building would be smart, but....)

You will probably have some different elements, but these can be a starting ground. read about heat exhaustion and heat stroke, and be aware of any of those symptoms.