"a sound that is like heavy rain/marbles hitting a tin roof or coffee perculating/heavy popcorn"
- sounds like a fun guessing game. Any more clues? What have you done to narrow it down?
Have you looked under the hood while revving the engine a bit or tried putting it in neutral or park and revving a bit? does it make the same noise then or only while driving?
In other words, narrow it down to drive-train noise or engine noise.
It could be differential/drivetrain related. On the engine side something on the accessory drive system? Its common the alternator pulley/dampener goes out. What about the fan clutch, if it was completely gone and falling appart inside itself it might sound like

Just some thoughts.

On the thermostat issue, its normal to run below half mark a bit, but not way lower.
- Mark