I had this problem on an ST2. Once you get into the loop of overheated rear brake it is hard to sort it because the following tends to happen:
Boil the fluid with heat passed back through the caliper
Heat buckles the disk causing small amout of friction
The heat build up causes the fuild to heat up and expand - if it is overfull then it has no where to go and the pads squeeze the disk enough to increase the heat, etc etc.
I'm sure you problably get the picture.
As for cleaning the pistons, I was also told a little brake fluid on a clean rag was the way to go. Shouldn't need grease, and definately not copper grease. The red stuff you refer to sounds like "Red Rubber Grease" and is worth having a tin of around. Our local dealer uses that for everything from electrics to 749/999 coil seals to well nuts - it's pretty safe. Not sure about how it might react with brake fluid on the pistons though.
Thinking about it - remove the caliper from the wheel and push the pistons out a little. Be careful not to push one ALL the way out - it is possible I did it on the ST2 and a sod to get back in. Wipe around the piston before it goes back in then alternately lever them back in and use the brake lever to push them out again. Sometimes hard to get both to work because one will move easier than the other. That might be the problem then in fact, one sticking piston.
Hope some of that helps, and does not confuse too much. Head full of cold so I am rambling even more than usual!
