In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how would you recommend me an approach (numerically and with each computational tool)? I thought about triangulating the points and using a unstructured grid Finite Volume Method. Considering the maths around this is a bit harder than that of a structured grid, I assumed the possibility of interpolating the unstructured grid into a structured grid, solving the discretized diffusion model and then interpolating back to the unstructured grid.
If you have a cloud of points and you don't want to use mesh-based methods like FEM or FVM, a possibility is to use a mesh-free method like the Finite Point Method. For instance, you could have a look at this article:
There are many other mesh-free methods, Finite Point Method is only one of them.