PG3: Not quite so pleasant: the test subjects didn't always make it through the allotted time in the hot bath, because they got too uncomfortably hot, but it still seems cheaper and more practical than paying out to go to a sauna (if you're not already a member of somewhere that has one) or running around in hot (for the UK) weather in a plastic suit or whatever.
Interesting recent research suggesting that it may be possible to get heat acclimated by sitting in a hot bath for an hour after a run: Zurawlew et al 2015, Post-exercise hot water immersion induces heat acclimation and improves endurance exercise performance in the heat. Scand J Med Sci Sports doi: 10.1111/sms.12638 (ahead of print).
The researchers were looking for something practical that might help. They got positive results from six days of a 40-minute run followed by hot water (40C) immersion for 40 minutes.
John 1946: My predicted time from a couple of methods is c. 10 hours, with less than a 20% chance, I think, of getting under nine hours. I'd rather be sure that I can (weather etc. permitting) cover the 56 miles reasonably than improve my speed but collapse at 40 miles because my base stamina is inadequate. If I hadn't lost large portions of the last two years to injuries (not due to running!), so I'd been keeping at the level of fitness needed for 50-mile races, then I might be thinking differently
I do my Wednesday evening runs with my club as tempo runs, and most of the routes are hilly and I'm pushing up those hills, and my ability to do so is improving and my speed is improving. I'm also running hard when I parkrun or run cross-country. My previous experience is that track work leads to injury, for me, so I'm staying away from that! If it gets drier then I may try some Yasso 800s (the field on which I normally do those is too wet at the moment for fast running).