Temperature distribution in solid represented by 3D point cloud

[Aorus]

Hello,
I have a large data set consisting of point coordinates in 3D (x,y,z), with each point assigned a specific temperature. The solid represented by the points is a cuboid, and I'd like to render it to show the temperature distribution on the surface of and within the solid (the data set contains points for the surface as well as the interior of the solid). All I've managed to do so far is render a point cloud using

xi = x(1):x(mx)/100:x(mx);
yi = y(1):y(my)/100:y(my);

[XI,YI] = meshgrid(xi,yi);
ZI = griddata(x,y,z,XI,YI);

mesh(XI,YI,ZI), hold
plot3(x,y,z,'.')

where x,y,z are the point coordinates and mx and my are the lengths of the x and y vectors.

I'm not sure how to use the colormap function to assign each point a color based on its temperature. The cloud is also extremely dense and impossible to rotate in real time. What I'd like is a way to just render the exterior of the cuboid as a smooth surface showing the temperature gradient. Of secondary interest is also a way of rendering various cross sections of the solid to visualize the interior temperatures.

Any help is greatly appreciated!