How To Creating Heatmap Over 3D Model?

Can anybody give me an advice?

Quite a few ways - you can for example use MeshStandardMaterial.emissiveMap, or just

Some points of the surface will have corresponding intensity values, how do I interpolate based on these intensity values?

So the heatmap is defined by distance from arbitrary points (and their assigned intensity) on the surface? How many of those points?

There is my example. Each vertex has a power value, however, you cannot get a heatmap with gradient.