The recreational center where I swim in the mornings has a bank of showers, and every one of them exhibits the exact same problem. If the dial of the temperature control were a clock, from midnight to 11:50 a.m. the water is tapwater cold. At 12:00 noon it is too hot to stand under.
Between 11:50 and 12:00, it gets lukewarm up to about 11:57, perfect at 11:58, and too hot to stand under at 11:59.
Why??? My shower at home gets 50% warm at 50% up, and between 50% and 100% you have plenty of room for tiny variations in temperature. That seems like a normal arrangement where hot and cold water are mixed at the nozzle. Why is a PROFESSIONAL shower in a PUBLIC FACILITY plumbed such that it's almost impossible to use the damn showers?
The showers at my old pool (near the old house) were even worse. There they had six showers on a pillar, and if you turned on only one of them you got nothing but ice water. If you turn on a second showerhead in the cluster, it comes on screaming hot -- but yours turns lukewarm. Turn on a third shower and you begin to get heat in the first shower. It was the craziest arrangement I'd ever seen.
I can't even IMAGINE what the piping must look like inside the pillar to make this happen.
And it'd been like that for YEARS.