I hesitated to reply. A 2 inch Forstner bit is fairly large. I assume you know the basics for drilling with a large Forstner bit?
* Make sure your bit is clean. Very clean. Sap, tar, and resin from green wood will be on the Forstner bit and increase friction a lot. Use a blade and bit cleaner. I have heard that Formula 409 (household cleaner) works almost as well, but have not tried it yet. Use a plastic or brass brush, not steel.
* Drill at a slow speed. For a 2 inch Forstner bit, the speed should be 500 RPM or lower. Maybe as low as 250 RPM. Some drill presses cannot go that slow. My old drill press was limited to about 800 RPM at its slowest.
* Drill only a little bit at a time, maybe 1/2 inch, then pull the bit completely out. If you're not actively cutting, then the bit should not be in the hole. The wood may tighten around the bit if it's stopped. If the bit is still rotating in the hole (but not cutting) then the spinning bit will create heat from friction.
* Blow out any shavings and sawdust still in the hole between drilling steps. I use an air compressor. Shavings and sawdust create friction heat when cutting.
* Allow the bit to cool between drilling steps. It takes much longer than you think. You must be patient; there is no magic. Your bits will last longer if you keep them cool, too. I try to speed it along by using the air compressor to blow air over the bit.
(I have heard of people using acetone to cool off their bits. I'd worry about cracking or weakening the bit with the sudden coolness. Maybe someone else here can share their experience with that.)