Force the state of floating digital input to particular level
This is a tough problem - If you can't physically touch the pin your options are pretty limited. And it sounds like you can't modify the software either.  I don't know what your debugging capabilities are, but can you run the SW/FW in some kind of debug mode and set up a flag or break point if the pin changes states?

if you want to heat/cool, you'd probably have to go outside the MCUs specifications to see anything happen, since it's designed to have the inputs working normally under its full specified temperature range.  That could be damaging to other parts perhaps or the MCU itself.  Even then it seems unlikely and unreliable.  

It seems unlikely that the QFN pin itself has enough iron/nickel/etc inside to be of any use with a magnetic field.  Perhaps as you surmised, some kind of electrostatic field might have an impact, but you'd probably need a really big one, and you'd risk zapping the board with an ESD hit.