The problem with cotton though is when it gets wet it's like wearing a straight jacket. You can't even move freely because it's stuck to you and now heavy with all that absorbed sweat. That evaporation process could take 2-3 days for a soaked shirt. Otherwise it's just sitting there wet.
I'm always amazed when people say they are coming out to go elk hunting and will be wearing all cotton. I always ask them to go outside and have someone hose them down in those clothes and then report back on how they can hunt like that. I never hear back from them.
If a damp t shirt presents that degree of physical challenge, perhaps some strength training would be necessary.
The OP didn't ask about general use, he asked about a very specific use under very specific conditions.