Another factor to consider is the surface area in contact with the belt. It's a LOT easier to overheat a piece of steel when there's a lot of contact. Dragging an abrasive through a large distance and creating a long trough (relatively - we're speaking microscopically, of course) imparts a ton more heat than just zipping it through a short one.
There's a similar analogy to the abrasive sparking situation for those familiar with machining - if there are any of you guys lurking about. Abrasives work basically like microminiature machine tools, producing microscopic chips and tool marks, etc.
Those with plenty of experience will have noticed how sometimes when roughing off a lot of steel on a machine tool without using flood coolant that sometimes the parent material of the work (NOT the chips, those are almost universally hot - they're analogous to the sparks in this theoretical analogue) can stay almost room temperature. Other times it can be so hot that water will sizzle if you dribble some on.
There are several factors here also, but some of the relevant ones are, again, the size, shape, sharpness and material of the cutting tool. The speed of the cutting tool and the angle at which it's presented to the work, etc. Also whether it's making point contact or broad contact, on the lathe whether the chip is thick or thin (high feed rate or low, deep cut or shallow) for milling tools whether the chips are thin on tool entry and thick on exit or vice versa (conventional or climb milling)...so on and so forth.
There's almost always a lot more going on with most any process than meets the eye. It's tough to get a handle on what exactly is going on in aa very deep way without quite some level of expertise/experience with the process and study of the principles behind it.