I do not think it is possible to achieve this effect using global volume mtl.
I think it requires some "fakes". Here is my attempt. So the "heat haze" effect is made using a cylindrical object with no caps which is at some distance from the camera, having a material with varied IOR just slightly above ground. The "mirage" is made using layered mtl, where base material is the sand and next layer is basically a mirror which is masked by falloff map which is white only at certain angles and at certain distance.
Please note that
a) the scene is pretty dirty
b) there are some crazy falloff maps used which I didn't think over very carefully
c) this setup might be a bit tricky in animation (the cylinder around camera part)