Did you turn up your hot water heater before your waterbirth?
My husband had grand intentions of doing this so that the tub idea would work out perfectly, but it turns out that I used all the hot water in the shower during labor and we didn't have any left to fill the tub. Luckily, it was a short labor so I was focused enough to not really care in the moment. I'm not even sure if we would've had time to fill the tub. Those things take forever!
We did, but we had to. It was a really old cabin in the mountains, in the middle of winter, with a small hot water heater. We had to fill the tub with hot (no cold), then wait 2 hours, then fill it up more with hot, then wait 2 hours, ... until it was full. I don't think the tub would have been as hot without turning up the water heater. Thankfully we got it filled before I started pushing. Just remember to turn it back down after the birth.