battery power?

Without the TV on, yes. It can be even quicker if the battery wasn't fully charged or is older.

I've been on all-day slogs through 100 degree Utah sun, LP mode not working and 12 gauge wiring on the TV, and watched the temperature go from 33 F (AC mode worked fine) to 80+. DC mode worked fine when the camper was plugged in and the battery was full when we left in the morning, and in good shape. After that trip I ran an additional 8 gauge wire in parallel with the 12 gauge line. I could have done it as a field fix but it just didn't occur to me that the TV wiring wasn't adequate - until I ran the numbers. 12 is just way too small and unfortunately it is what you get from vehicle manufacturers and aftermarket places like Uhaul.