Naio,
Heating pads will help--but tend to warm the air. The newer ones tend to have a built in timer--so they shut off after 3 hours. Most probably the new ones won't "like" MSW inverters. The cheapest ones from Walmart don't appear to have timers. The largest ones from Walmart have exactly the same wattage as the small ones. Weird. Install a grate at the top of the cabinet to allow warmed air to flow out of the cabinets. I have a couple from Lowes and they are quite decorative.
If the fan works, then plan on installing computer fans--they are inexpensive and don't use a lot of power. Make a grate on the bottom of the door and place the fans at the top to suck air into the cabinets.
