Mapping external data to a mesh

I’m am trying to figure out the best approach for color mapping external data to a mesh. For exmaple, I have a mesh that represents an object like a car engine, and I have data (from a file or other data source) that has location information and associated temperature that changes with time. I want to “layer” the data as a color map over the mesh and have the ability to watch the temperature/color change over a time scale. What is the best way (or any way) to do this? Do I modify a texture or material of the mesh with each time step?

Thanks for any ideas or insight!

Yes, change the colors per vertex on the mesh
Probably want to use a Vertex Lit shader too.