I'd probably put one in a wider bucket (trug or similar? ) and place the brew bucket in that so it acts as a water jacket.
Various people on the brewing forums advocate exactly this. It also means if the heater fails, it won't risk contaminating the beer.
OTOH, it's a less efficient way to heat the contents of the vessel and for me, the risk is low enough to make it worthwhile. As for sterilising, it's just a case of dropping it in the vessel along with all the other bits you're sterilising.
You wouldn't necessarily need to modify the lid either - just leave a crack for the wire to trail over the edge. The blanket of CO2 generated by fermentation will protect the brew from oxidation. You could put a bit of clingfilm or something over the gap to stop creatures getting in if necessary.
Still pressure being generated so bottling is a few days off yet.
Don't rely on this as a guide - use a hydrometer to be sure, especially if you're bottling.
Talking of bottling, using the barrel as a "bottling bucket" is exactly what I did with my first brew, which is the only one I've bottled so far. The main reason being that it has a tap, so it was much easier to fill the bottles than fannying about with a syphon tube in the fermenting vessel.