This was in September on the Aragonese but I think it safe to say that there will be rain at some point in Galicia, and he will have kilos of mud on the hem of his cassock. Or maybe not. As far as heat goes, if the cassock is cotton or a fine light wool, it might even be cooler (I have clergy friends who tell me that this is so, and certainly in North Africa the jellabah/galabea seems to serve as a practical garment in very hot weather).
My advice, for what it's worth, is to tell him to forget the cassock. In theory, it is the normal streetwear of the clergy, equivalent to a business suit, and I have yet to see anyone in a business suit and tie on the Camino. I do not want to sound offensive, but I do not know if doctors feel more medical if they wear a white coat on the Camino, or if lawyers feel more professional in gown and bands. My advice (which he can ignore if he wishes) is that If he wants to feel more priestly, he should carefully say his offices (for Anglicans, matins and vespers; for RCs, their breviary) every day and look for ways of being of service to others along the route. He should perhaps seek the opinion of his spiritual adviser or mentor to get some ideas which would be tailored to him and his needs.
The several clergy I have met on the Camino told me that they found it a very welcome place where they could re-examine their vocations within a spiritual environment but without a spiritual structure around them, and they found it freeing when they could be seekers along with the others.