Truthfully, I'm not sure why the tool tries to bind in the groove. Heat may be the root cause of the issue in some other fashion, but I don't believe thermal expansion is. I can see how you're visualising the side of the groove encroaching on the tool, being that the part is expanding in every direction as it heats but it doesn't work that way. A good analogy is a bearing pocket. If we make a press fit pocket for a bearing, then heat the part significantly, it will expand in every direction. However our pocket is now larger than it was and our bearing drops in with no force required. In this case the sides of the part do not expand inward to reduce the pocket diameter. And I agree the tool will be heating and increasing in size also, but the coefficient of expansion is far less for the tool than the workpiece (around half) so clearance should still be increasing. Doing the figures on steel, a 2mm wide parting blade will expand its width about 0.0026mm if increased in temp by 100 degrees C. Half of this expansion would be towards the chuck where the work is fixed so there could be some rubbing here, but as the groove itself has opened up, the tool should be free to flex and stay in the groove. It's my best guess that the cutting chips are responsible for the jamming rather than any expansion.