This is just something that I thought up while doing busy work at my job. Is the sensation of heat simply coming from particles colliding with your, say, hand? Are they transferring energy more to objects because they have higher velocities, and thus heat can hurt? (Sorry, this isn't a more cohesive question...).
Heat transfer occurs when particles collide against an object (which is made of other particles) or when photons impact on the object.
Temperature is a measure of the average amount of kinetic energy of the particles (in a gas this will be simple related to how fast the particles of gas move but in a solid it will be about vibrations of the particles).
The sensation of heat is a product of both thermal radiation (infra-red photons are emitted by the hot object and absorbed by your hand) and contact with something that can transfer some of that energy directly (hot gas particles or a hot solid directly touching your hand). Living things have evolved to sense heat and cold because they only survive if they avoid extremes of both.