mm wrote:

In high school physics, the three methods of heat dispersal were
presented as conduction, radiation, and convection?

Is that all there is? Is diffusion a fourth or is it subsumed by
convection?

It's a part of conduction. Some people also add "phase change" as
a method of heat transfer, eg evaporation from lower soil layers
and condensation above.

As to convection, it was always described and seems to be limited to
broad currents, such as hot air rising and cold air sinking, but is
that all that happens? In, say, a room with moderate cooling in the
summer or moderate heating in the winter, while in general the hot air
rises, doesn't the random motion of some of the hot air cause it to go
downward and to mix with the cooler air below it?

Not much. Then again, room air may fall near an outside wall, slide
across the floor, rise up near an inside wall, then slide across
the ceiling to make a loop.

Is this radiation?

No, but that can also be important. Surfaces with mean absolute temp T (R)
and emissivity 1 have a linearized radiation conductance 4x0.1714x10^8xT^3
Btu/h-F-ft^2, eg U1 (R1) for T = 400 + 70 (F.) = 530 R.

Nick