A thermostat isn't a thermometer. A thermostat will keep the under tank heater from going wonky and burning your snake. I measured the temp on mine before I hooked up a thermostat and it was registering at <130. If it feels hot or warm to you, it's TOO hot.
Pinkies are way, way too small for a BP. They can handle rat pups and adult mice right out of the egg. Prey size goes up as they grow - this is likely the source of him not shedding; he's not getting the amount of food he needs to grow. Prey size should be the same width as the WIDEST part of his body (not his neck). For him, looking? Probably rat pups, maybe even weaned rats. Definitely, definitely, big enough for large adult mice.
This is what my older snake eating looks like - and appropriate sized meal (small rat). It looks LUDICROUS because the snake's neck is a quarter the girth of the rat.
They're really stretchy.