I've done my C-41 wash with cold tap water (60+ F) and final rinse at room temp (around 67F that day), seems to be fine. What I did in my last batch of C-41 was adjust the hot and cold taps to feel close to the tempering bath. Doesn't need to be exact.
If hot water tank capacity is the major issue, don't bother with another sous vide, just fill that bucket with tap water adjusted to roughly right, and do an Ilford wash from it. Fill, invert 5 times, dump. Fill, invert 10 times, dump. Fill, invert 20 times (optionally let stand a while, not needed but won't do any harm) and dump before final rinse. This method is so water-efficient I've used grocery store distilled water for the entire wash without pain (a half liter tank fill for 120 in a Paterson will wind up using just two liters, including the final rinse). Could just stand a jug in your tempering bath alongside your process chemicals, too.