I've had the same problem with my 2007 V6 with manual air. I first noticed the problem a few months ago, when it was still reasonably cool, but my black Explorer got hot during it's sitting during church. So, that eliminates the heating problem.
I live in an area with many long hills and it too was intermittent. I checked all the lines under the dash (that I could reach with the glove compartment down) and found nothing loose. I then found that the grey line, which runs back out the firewall and to the front of the engine, had come loose. I reattached it and tied it up with zip-ties to prevent that happening again.
Everything seemed fine until a couple of weeks ago and it started again. I went back to the check valve and it was ok, but I decided to start the vehicle and see what kind of vacuum I had on that little line. There was vacuum, but weak. I followed the lines around to the plastic box where all the vacuum lines seem to start and it seemed to end at a ell shaped rubber adapter just in front of where the brake booster vacuum line goes. There were three lines going into this ell and all seemed tight. I decided to disconnect the ell and see if there was good vacuum there and there was. I looked inside the ell and could see the end of the larger line of the three, but one of the smaller ones (which did not come inside the ell) seemed to have a flap of rubber over the place where it should have come out. I removed this flap and pushed both of the smaller lines completely in to where I could see about 1/16 inch of the end inside the ell and re-installed the ell to the "box".
Rechecking the line near the check valve, there seemed to be an increase in vacuum and I have not had a recurrance of the problem.
Hopefully, I have found it, because I have experienced the "can not reproduce the customer's complaint" many times and know your frustration.
Good Luck.
