Well, I've had the radio running all evening and the can didn't even get slightly warm, but the hum is pretty noticeable. In fact the only thing that did get hot was obviously the dropper and the stuff around it, including the two nearest valves, which I assume is what you'd expect. I also moved the radio to a worktop on the other side of the room and the reception improved a fair bit on MW, so it looks like my kitchen table is a poor reception area, however there was no noticeable improvement on LW, which is still just a mass of static.
Anyway, I'll probably have another tinker with it at some point tomorrow