Four Bettas in a 10 gallon tank? I guess if you must, but you really will need to monitor their water daily and do daily water changes to keep levels of ammonia undetectable, and then nitrite which will follow that, in days or weeks, undetectable - by doing water changes to accomplish that.
+1 What BFM just said, and what everybody else said. Daily water changes on a 10 gallon tank takes very little time. I think if you get an API Master liquid test kit and test your water you are going to be astonished at how much ammonia your fish are living in.
No one is trying to bash you: it's just frustrating when you are asking for help and people are just trying to help you and your fish by telling you the truth.
Your Bettas can't tell you their skin and gills are burning, and, yes, they can live like that for quite a while, some longer than others, but what a life. As was mentioned finrot is a direct result of poor water quality.
Also, as mentioned, if the temperature of the water change is more than 2 degrees different (and I think even that's too big a difference) than the water they are in, yes, that would be very stressful and, in fact, can have serious health consequences.
The only motive of the people that have been responding to this thread is to help you and your fish, sincerely. I'm still a noobie, myself, but I've learned from the greater experience of the fish keepers here on AC. I hope you take the advice in the spirit it is offered.