Yep, the hair dryer will do it every time. Also the coffee maker or any other heat generating source if the electric heater is on. We've been known to get lucky using our regular oscillating electric and a very small little electric cube heater near the rear bunk, but that's as good as you're going to get.
Last years FL spring training trip could not have been much colder....for FL in Mar. Down to the mid to upper 30's at night. We left home with both tanks full, ran with the propane for the frig on the road, used the stove and oven every day, ran the furnace every evening and overnight and the last night enroute home DH manually swapped tanks just so he didn't have to go out at 3:00 in the morning to do it. Found we still has a small amount in the starter tank. We were gone 10 days. So, yes, it does cost extra rather than using the campground electric, but it's not terrible and I'd much prefer to be comfortable rather than shivering for maybe $25 or less. BTW, don't know if all CWs do this, but we found one with propane fill ups for $1.99 per pound/gallon/whatever on Tuesdays and Wednesdays, I believe....or maybe Wednesday/Thursday. Might be worth a check. Of course, we missed it by 1 day. Usually our local U-Haul is the best deal. Most of the places and our dreadful RV dealer charge a flat fee of $20something if it completely empty or you just need a top off, so check around.