If a propane heater aka "furnace" is properly designed for an RV and
properly installed (vented etc) you can run it all night, though most
go on and off via a thermostat.

How often do you hear of American style campervans blowing up?
(most of them have propane heaters and hopefully a CO2 detector too)

I bet more Vanagons burn up due to fuel lines than ALL campervans
with propane furnaces.

my $0.02