Can you have any kind of "snap" other than a cold one?

"Cold Snap" does in fact refer to the speed at which the coldness arrives.

From this source -

Also, cold spell .  A short period of unusually cold weather, as in The recent 
cold snap has threatened the crop . The first expression presumably likens snap  
in the sense of "a sudden bite or cut" to sudden unexpected cold. The variant is 
more obvious, spell  having been used in the sense of "a bout or turn at something"
since the early 1700s. [Early 1800]

And certainly you could find the phrase "Heat Spell" or "Warm Spell", and you'd certainly be understood if you referred to it as a "Heat Snap".

But the phrase has roots in reference to a sudden onset of cold, in the same way a "Heat Wave" holds a different meaning specific to heat. You could refer to a sudden and lingering onset of cold as a "Cold Wave" and be understood, but neither "Heat Snap" nor "Cold Wave" are common terms, and referring to them as such would be unorthadox.

I think "snap" (as in "cold snap") is used only to refer to sudden and drastic decreases in temperature because some materials get very brittle when they suddenly get very cold, and may actually snap and break apart. For example, when the leaves on the ground get very cold very suddenly, then make crunching and snapping noises when they're frozen.

If something that is already cold warmed up too quickly, the sudden change in temperature would damage it, but I'm not sure it would snap, it would probably just break or fall apart. When the leaves warm up suddenly in the spring, they don't really snap apart, the just sort of turn to mush.

The more I think about it, the more I think "cold snap" refers mostly to organic matter, where the cells expands rapidly and then burst when the object freezes. As long as it's frozen, it's "crunchy", but if it warms suddenly, it turns to mush, so a sudden warming isn't a "warm snap" so much as a "warm mush".