I have a similar issue in my 06. On particularly hot days (such as this afternoon) my turn signals won't work. I'll get the "quick flash" and the "light burnt out" dummy light. Then after a while, they work.
I've been having this problem for about a year now, but have been too lazy (busy ? ) to pull out the volmeter and really troubleshoot it. Plus, it's "fixed itself" by the time I get home, so I've never actually even been able to jump out and see if it the bulbs really aren't working or not.
I suspect a bad solder joint, based on an experience I had with an old Honda. On that car, on particularly hot days it wouldn't start. Like literally turn the key and nothing ( no cranking) would happen. But leave the doors open for a few minutes, let the car air out, and it would start. Weird, right ? Turns out the main relay had bad solder joints, and over time the joints developed microscopic cracks. When it got really hot inside (like 100+ degrees) they would expand to the point where the cracks were large enough to not pass electricity. FORTUNATELY this problem was pretty well documented online and the solution was simple: remove the pdb, desolder and resolder everything (with better solder joints

I did that, the problem never recurred.
The symptoms I'm experiencing are so similar - intermittent only on super hot days, self fixing (presumably because the AC is running) - that I suspect a similar issue.