Just wondering if I need to pull out and replace an old plastic electrical wall box that sits a good 3/4" behind the drywall? Seems like you would want a tight fit for heat sealing, but is there an electrical code reason? Box has three 10-2 romex cables with grounds for a 240v thermostat. It is on an interior wall. Part of me wants to get a deeper plastic box and part of me wants to just install the thermostat the way the box sits now...
You need an extender
Assuming that your 3/4" "behind" the drywall means that the box is recessed into the drywall, you will need a box extender to fix the situation, as per NEC 314.20:
314.20 Flush-Mounted Installations. Installations within or behind a surface of concrete, tile, gypsum, plaster, or other noncombustible material, including boxes employing a flush-type cover or faceplate, shall be made so that the front edge of the box, plaster ring, extension ring, or listed extender will not be set back of the finished surface more than 6 mm (¼ in.).
Installations within a surface of wood or other combustible surface material, boxes, plaster rings, extension rings, or listed extenders shall extend to the finished surface or project therefrom.
Fortunately for you, plastic box extenders are cheap as chips at any home-improvement store and should serve you just fine in your application.