HiCustomer.. welcome to Just Answer!.
I have to tell you that this isn't something that happens often and can be a bit of a mystery. I've only recently been involved in two confirmed fixes for this type of problem, one on a Caravan and one on an Intrepid. Both vehicles would drive fine for a certain distance, then the brakes would begin dragging as you've described. Later... checks OK once cooled down.
Each needed a power brake booster. Each had fluid accumulation within the cavity... one was brake fluid, the other (Intrepid) was water.
What's happening is the booster is holding the brakes on just ever so slighly. Actually, not at all at first as there's no brake drag, but it's holding the brake master cylinder piston forward just enough to cover the compensating ports in the cylinder, which prevents fluid from returning to the reservoir.
It allows normal pedal functions until heat at the wheels from normal braking expands the fluid, which travels backward to the master cylinder... expecting to be vented into the reservoir bowl.
But it can't make it back, since the compensating ports are blocked. This means fluid pressure begins building from heat alone and then the real heat begins with unintended brake drag, which quickly puts an end to the trip.
One thing that worked as a diagnostic aid on the Caravan was removing the vacuum check valve from the booster at the moment when the van would no longer move forward on its own. This vacuum release repositioned the internal pushrod just enough that the van released its brakes and became mobile again.
Another diagnostic aid would be to loosen the two 13mm nuts holding the master cylinder to the booster by several turns to see if the extra spacing accomplished the same thing. You won't be able to drive like this, but for diagnostic purposes... should be effective.
ABS and mechanical sticking of the calipers are extremely unlikely, as neither instance of this sort would allow normal braking for a fraction of the distance seen in my two cases.
Short of a fluid contamination situation (which swells rubber), I'd look into the booster.. literally. Pull the vacuum check valve and drop a dipstick of some sort into the chamber to see if you have fluid in substantial quantities lying below. You could even use a trans or engine
dipstick (if cleaned). The rubber seal on the inside of the reservoir cap is a good source of information when it comes to contamination... it'll swell to twice its normal size.
If you have any questions, don't hesitate to write back. I'll be glad to help.