Definitely wait on that thermometer. A lot of use that specific type of heater, and I've never had anything that bad.
Well, I live in Texas and it's April. I don't even need a heater, but it's for the sake of night-time drops, haha. It gets bad in the day, but normally because it's pretty warm inside the house, it stays around 79-81.
Exchange the heater. Either wait 24 hours for the thermometer, or exchange the heater tomorrow for a new one. My walmart ALWAYS has at least ... a bajillion in stock. They sell quite well.