Our gas engine van came from the factory with sound damping and insulation. I would think the diesels would have even more - maybe yours is missing? I disassembled ours and added a mass-loaded vinyl sound barrier between the factory damping and insulation, then re-installed the insulation. It is quieter but I wasn't concerned so much with heat.
There are spray-on materials that claim to do both.
But the biggest noise reduction is to make sure the engine cover is sealed tightly to the floor - any gaps let lots of noise through.
I haven't taken it off again to see if it's still glued on.
Here's the factory job
And after I added the MLV. I glued it in and then sealed with metalized tape.