I think it is a combination of heat and humidity. I am not quite sure what RSL is? Is it red sex link? Cause if so, them and the EE I have and had no problem with, we frequently get above 100. But very low humidity, very very low, as in less than 25%.
In high heat they do need water, shade and a air circulation.
ps. I never worry about my chickens. I just let them be chickens.
I have an Americauna, I know... it's not an EE, or is it? It is the heartiest of my flock and I have a good buddy with several RSL's and they do just fine in the Arizona heat! Relax. They pant too keep cool just like a canine. Your birds will be fine. Just make sure to have plenty of fresh water for them and some nice cool lettuce and such for treats will help them out tremendously!