No, modern-day processors are actually designed in a way that they do not heat up while performing ordinary tasks. As opposed to the older days, when even word processing would heat up a laptop randomly, the technology today is way better and your laptop remains cool during most of the operation.  Even if it does heat up, today’s laptops come with smarter heat vents that are designed to keep the system cool, so your laptop heating up is something you shouldn’t worry too much about.