It is difficult to answer without assessing Jesse's coat in person and knowing the typical highs (temps) of his climate, his living conditions (night turnout? fan in stall? etc). Its perfectly OK for a horse to sweat; that's the normal cooling mechanism of any healthy horse. However, if Jesse is repeatedly sweating while at rest to the point of overheating (panting, body temp > 104F), and doesn't have a way, or good sense, to access a cooler spot, then yes, he would probably benefit from a full clip. He's TB, correct? Typically this breed does not have as much trouble dealing with heat as would a heavier horse such as a Draft or well-muscled QH.
I have three horses I care for: my draft mare from Canada gets full body clip year-round b/c (1) she does not handle heat well b/c she's heavy, (2) I compete year-round; (3) I hate hair. This mare will (& has) easily overheat just by standing in the full sun on a 85F day. Luckily she's smart about standing under her fan in her run-in. My Saddlebred, however, has no problem or sense of standing out in the same blazing hot weather sweating up a storm. Likely his Arab ancestry lends to his easier coping with heat vs my heavy Canadian draft mare. The TB I ride can be ridden for hours in 95F heat and barely raises his respiration efforts bc his systemic sweating mechanisms are so efficient. He sweats ferociously but quickly dries; sweats & dries, etc.
So really its an individual decision based on climate, workload, degree of PPID progression (more advanced cases have thicker, coarser coats that don't shed), breed/heat tolerance, and possibly by owner preference.
Just remember that a full clip isn't without its downside, meaning less protection from flies & sunburn, which some horses can't/won't tolerate (TBs in particular!)
Kerry in NY