It's going to lose a lot of temperature on that journey due to turbulent flows and mixing of steam with the air in the room, even over short distances.
Understood, but if it's still steam and not water when it comes into contact with the handle, it's still not lost enough heat to be under 100c. It shouldn't matter how hot the steam is when it comes into contact with the handle, provided it is steam. It will release heat when it condenses, and anything it is in contact with will be the first to benefit from that heat. The question is if that heat is significant enough to account for the noticable increase in temperature.

I feel like it must be, because logically one would expect the handle to become cooler, not warmer, as the metal pan loses heat to the water. If we can't find another method of warming, then are we to assume it's a psychological thing? That it is a question of our perception of heat? That seems even more exotic than my proposal.