Should I let the jigsaw blade rest once it heats?
Not usually, no. It's perfectly normal for jigsaw blades to get hot in use.
Even hand saws can get uncomfortably hot1 if you're sawing enough and any traditional saw is made of plain carbon steel. Modern jigsaw blades should be made of much more heat-tolerant alloys that don't care even a little about running hot, up to about the temperature that you scorch wood.
If you are getting smoke2 it probably indicates you're running too hot, in which case you can take a break or cool the blade down by swabbing it with a damp cloth or dipping it in water. This won't harm the blade, any more than dipping chisels in water periodically during grinding does — despite tales to the contrary3 — and again most chisels are not a modern alloy.
One thing to note in relation to jigsaws specifically is the relatively thin blades being held at one end only mean they work best if they're run at their 'natural pace', and that pace is, um, not fast4. Try to let the saw do the work; remember that it's not a race. It's hard to describe how this feels in words, much easier to demonstrate in person (as it was to me), but you should experience little resistance to forward motion of the saw. Imagine controlling the saw with one hand and pushing it forward with just one fingertip of the other hand and that might give a good impression of how much forward pressure you should use.
I'm learning mostly through YouTube
You didn't ask about this but I wanted to address it in the context of power-tool use. Be very careful who you learn from! There are more than a few high-profile YouTube woodworkers and makers who have awful shop-safety practices.
Try to learn to identify who they are and not pick up their bad habits!
1 Drill bits being driven by a hand drill can too, and much hotter, and it is rare or unheard of for modern bits to be cooled except to make them comfortable enough to change if the user can't or won't wait for them to air-cool.
2 Use your nose, not your eyes, to determine this as there's no mistaking the odour.
3 Although there are seemingly logical explanations about how it can occur it has never been demonstrated to harm the steel in normal grinding operations, and, dipping in water has been standard workshop practice since before any of us were born.... if it did cause a problem someone would have noticed and we'd all know about it by now :-)
4 Except in thinner material and soft woods. With thicker and tougher material (and 20mm chipboard definitely qualifies) the cutting rate should actually be quite slow.