Can I use a propane or ventless heater in the room while epoxy cures?

Yes. Any fumes given off by the epoxy are not flammable, so there's no risk of them igniting. Using a space heater, including a ventless propane heater, to hold the room at the 75°F minimum that UltraClear Bar & Table Top Epoxy needs is common practice; we and our customers have been doing it for many years. The epoxy can also be used safely in a closed-off space, such as a basement with no real ventilation that's warmed by a small blue-flame ventless heater.

If you can't heat the whole room, tent off the area around the surface and run space heaters inside the tented-off area to keep it at 75°F or above for the full cure: https://ultraclear.helpscoutdocs.com/article/208-epoxy-temperature

UltraClear Deep Pour Epoxy has a different temperature target. You don't want Deep Pour to overheat; cooler is better, with 60–70°F being the sweet spot. If you're heating a shop for a deep pour, keep it in that range rather than at 75°F. Deep Pour Epoxy instructions: https://ultraclear.helpscoutdocs.com/article/840-deep-pour-epoxy-instructions