Yes, BPA would leach more at high water temperatures. Whenever I repurpose any container, I run it through the dishwasher a few times. Whatever might leach in use would be reduced by the temps and (more so, due to complicated factors in the diffusion of chemicals through a solid) because of the detergent in that hot water. I am NOT saying it makes it totally safe, only that it removes some of it and I'm comfortable with the remaining risk. You probably got more BPA exposure from the last receipt the grocery store clerk handed you.
HPDE is good stuff. I sometimes go dumpster diving at the recycling center for HDPE containers for all sorts of purposes - BP storage, bowl use, portable one-tank refueling for pre-mix fuel for my chainsaw, etc.
HDPE is used in water storage containers, gasoline storage cans and has a wonderful temperature range. It is used in "tupperware" sea kayaks, even more river kayaks, and as sled runners in the Iditarod (which get banged around at -50F). You can heat weld it, saw it, sand it, or use a sharp knive/plane to form it. Some plastics get brittle at cold temps (especially PVC), but HDPE does not. LDPE is used in some food containers as well, but isn't nearly as solvent/fuel resistent so I don't bother with it.
My favorite plastic-fabrication trick is to take a strip of any HDPE container, light it on fire at one end and let the molten plastic drip onto the surface being repaired. I've fixed ski kayaks while still on the beach, downhill ski bases, and once, a bear-chewed nalgene using that technique. Sure, a hot-air plastic welder is more controlled and leaves no soot, but is not nearly as fun and you can't do it at 12,000' or on a remote island.