Running that or one of those little space heaters seems to be what many people do but I really don't think it is the safest option. Something radiant like a seedling heat mat or reptile heat pad seems much safer.
I think the heat source should be just adequate to maintain temps down to the lowest ambient temp you will see. For a chest freezer to stay say 60F inside even at 20F ambient, even 50 watts should be plenty adequate.
For one thing if for some reason the heat gets stuck on, if you have a hair drier going in there, it's going to get really hot really fast. If a 30 watt reptile heater gets stuck on it will get a bit toasty in there after a number of hours, but nothing like an 800 watt plus hair drier going in there.
Also would have to check your thermostat relay rating, most hair driers it seems even on low they might still be 800 watts, on high they can be 1800 watts on some of them.