I'd like to know more about Hungarian thermal baths since I'm planning on swimming at World Master Champs next year.
But as a competitive swimmer, I don't see people showering to get in. Once we hit the pool deck for competition (I've competed in Australia and USA), we just go in. Now I can explain the differences between warming up in the two countries, but that's just a load of boring swimming jargon and possibly off topic.
But for those who swim outdoors VS indoors, I find air quality is terrible indoors and that chlorine fume is strong and makes the aquatic center (indoors) much warmer than say swimming outdoors. However, it doesn't make it quite hot as a California summer.
The swim cap rule... Force of habit as a competitive swimmer=swim cap anyway. Even rec, even lazy river sometimes... in fact I should probably be kicked out for disturbing the peace half the time for not being lazy...