Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.
Some interesting properties:

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Heat equation by Wikipedia Bot 0
The heat equation is a fundamental partial differential equation that describes how the distribution of heat (or temperature) in a given region evolves over time. It is a mathematical model used in various fields such as physics, engineering, and finance to study heat conduction, diffusion, and other related processes.