Adjustable Heatmap blob effect

You can modify the base set-up in any way you see fit in the pre-comp. If you need separate temperature ranges to behave differently, simply create them as separate layers^with a controlled fixed coloring. Heat waves can easily be created with Roughen Edges and sandwiching in a layer between the "colder" outer regions and the hotspots would be easy enough. Again, the point is to just play around with this and get a proper greyscale input map from the pre-comp.

Mylenium

You've similar ideas. Although it gets close, still isn't perfect yet. So more ideas are welcome :D.

Create whatever shapes you need in a pre-comp, blur them like crazy with a Box Blur with at least 3 iterations or Gaussian Blur  and apply a Colorama/ Tint/ Tritone or whatever effect.

Mylenium

I've recently been playing around with something similar for a different end result.  What I ended up using a shape layer with a black&white gradient fill.  The shape layer let me control the shape so it wasn't perfect.  I then applied the Colorama effect to the layer, which gave me a range of colors.  

I imagine the Fire preset in the Output cycle might get you close and if not, it is hopefully clear how you can build your own "heat" palette.