Just for some reassurance, unless the built-in tank is really tiny, I don't think you have anything to worry about for a week under the conditions you describe. Colder weather when the furnace would be needed all day is of course a different matter entirely; but having it run for a few minutes every hour or so during the night isn't going to use an enormous quantity of propane. One pound of propane produces a little over 20,000 btu when it burns, and one gallon about 90,000 btu; with a 30,000 btu furnace, that's about 40 minuts of runtime per pound or two hours per gallon. If you're needing it only at night, presumably the duty cycle would be relatively low (five or ten minutes of run time per hour).
By way of comparison, a pound of propane also roughly equates to a day to a day and a half of fridge operation, or two to three hours of water heater operation.
