The 80 C test was successful. I did insert the tub into a styrofoam container. The container is a common one here in China used for shipping meat, basically a big, square styrofoam cooler, with a lid. This does help keep the heat in, I think, though it wouldn't be as efficient as a purpose built ice chest.
If you want to do this and also have something that could work for sous vide (i.e., a high heat environment), you might consider starting out with an ice chest, instead of a plastic storage container. It should be much more energy efficient. the reason I shied away from them is that they tend to be pretty deep (high walls, narrow footprint), which I find a bit of a bother when processing film. A more powerful heater might give you some comfort too. I think it is important to make sure that the water flow can move the heat into the bath efficiently. If you have a big heating element, you might need more flow.
The last thing I want to add to this are a couple of shields to protect the heating element and the temperature probe from being banged about. The probe in particular is easy to bump, and it has a lot of leverage against the very thin through-hole in the wall of the container (I should probably reinforce that hole a bit better than I did).