Should be. The skin can be a little sensitive after but you shouldn't have any problems moving him to another enclosure so you can change his tank around.
You don't want your thermostat probe getting wet with urine or urates or something so that's why you generally don't place the 'stat probe inside. Your thermometer probe should be inside, placed right against the bottom over the UTH and tacked down with hot glue. That's because BPs burrow into their substrate and will lay as close to the heat as possible. You want to measure that spot so you know just what temperature your snake's being exposed to. You're less likely to get the thermostat probe moving around on you when it's between the bottom of the tank and the UTH. If the probe gets moved and is dangling in open air the thermostat is going to try to compensate for what it thinks is the improper temp by blasting the UTH at full power, which will lead to burns in the long run.