Old school dimmers don’t need a neutral or pull a neutral to the switch box from the easiest most accessible plug or j box. If there are two sets of Romex in the switch box one of the whites is likely a neutral. Quick check with a multimeter…

Black= current carrying conductor, white= grounded conductor (neutral) bare= grounded conductor which is bonded to the white in the service panel.

No need to de energize the low voltage from the thermostat but be careful not to short any of the small wires together or you’ll be tracking down your power supply and replacing the fuse.

I would get a digital amp meter and ensure the current is within 80% of rating. If the switch is rated 15 amps, ensure your only loading it to 12 or less.