It really warms as it collects moisture. I'm not talking about reactivation. It is transient but you can sense it when compared to entering liquid temp going into the drier. It does not affect drier performance and it is very transient, it will make you scratch your head cause if anything you would expect same temp or a drop if it is restricted.
You can also demonstrate it by opening a new replaceable core and holding it in your hand, if there is enough humidity in the air you will feel it warm up. It won't be any good after that.
I have observed it like on chillers that had a rupture and your replacing drier cores every 30 min.
Years ago Sporlan had a white paper on it and RSES referenced it in a SAM Sorbents and Desiccant.
I will try to find I not sure it I'm not sure it is archived in on line stuff, it really old like late 60's
You all are right the warmer the fluid the less water the drier will adsorb.