I have a Hearth & Home Heatilator NNXT3933. It came with the RC200 remote. I would like to get the RC300 which has the built in digital thermostat. The part for the Heatilator RC300 is RC300-HTL. I have a bead on a RC300 for Heat & Glo - also made by Hearth & Home. That part number is RC300-HNG. The only difference I see is the labeling on the remote. One is badged Heatilator the other is badged Heat & Glo. Any chance the Heat & Glo would work with the Heatilator? I'm guessing the innards are all the same. Thanks.