The charger for the batteries will be powered by a PC power supply, of which I have several lying around spare. But it's occurred to me that I can be a bit more clever with this.
I have three temperature sensors; one of these is continuously telling me the outside temperature, and two are telling me the temperature in the Data Shed. I can divert one of those two, and use it to take the temperature of the battery while it is being charged. And I can monitor that temperature from, say, a Raspberry Pi, and switch the PSU off if the battery is getting too hot. I can also use the Pi to power-off after a preset time.
The iMax charger will, I think, be able to do all that itself. But it's more fun if I set it up myself.