I've never had much success with keeping lather hot or even warm. I suspect it's the fact that I live in an exceptionally hard water area (if you look on the maps of water hardness most of East Anglia is in the hardest category). I find that trying to keep my lather warm, no matter which soap or cream I use, just causes the lather to collapse into a frothy mess.
That said, many people do have great success with keeping their lather warm. The simplest way is to place the mug in the basin of hot water you use for face and razor rinsing. Alternatively, a scuttle (specifically a Moss-type scuttle as opposed to the old-fashioned soap scuttle) is a popular piece of kit. Several people make them, but many of us recommend Steve Woodhead - I have a lather bowl from him as opposed to a scuttle, but the quality is the same and I love mine for cream lathering. Alternatively, if his prices are a bit steep for your budget, two containers where one will fit in the rim of the other so that you have hot water in the lower one and lather in the upper can work well, though stability issues may arise if what you're using as a lather bowl doesn't fit well inside the hot water container.
As for the mug question, though I'm not familiar with the EJ mug, I suspect that, if you want something much larger, you might have to look at a small lather bowl or scuttle. Steve Woodheads' bowls and scuttles do both come with handles, so if the lack of one is your only objection to a bowl or scuttle then it need not be.