Probably best left rugless while travelling, imo, but may benefit from a light fleece/sweat rug after unloading to help with the drying process. You will need to look for one that fits your particular animal, so tbh I don't think recommendations will be much use.
I would personally rarely leave a horse rug less on transport - although I do know that international transporters insist on it. I have just seen enough accidents to know I would rather rip a rug than the horse's skin.
Clipping helps obviously. If you are regulalry transporting a fully coated cob they are going to sweat up. And - what I said above notwithstanding - they probably have enough coat to protect themselves. Assuming they are fully clipped but stressed...
You can get ultra light scrim type wiking rugs. Ours are Amigo - but others do them. It will pull the sweat whilst minimizing the marking on the coat. If it is cold / windy a thermatex or similar on unloading will help dry once off - or the newer microfleece ones.
For better reccomendations - why are you travelling your swety cob? And is he clipped out?
I usually travel naked, but if my mare is wet when she goes on (washed after work), I use a half fleece half mesh fly rug from Kramer. A full fleece / sweat type rug would make her too hot and sweaty, but the half mesh seems to work well.
I travel my girl in her Amigo stable sheet. its such a thin, cotton material it works brilliantly. It is brilliant for moisture control so when they get warm/sweaty it lifts it to the surface and leaves them comfortable and as dry as possible.
Although, my girl is an angel to travel. She is a warm horse, so occasionally gets a little warm https://www.derbyhousestore.com/en-...MIy-Hgnfz54AIVbL7tCh3U7A3XEAQYByABEgJdZ_D_BwE
I have a Mark Todd thin waffle type rug which is great for travelling in summer. I have one who sweats up a bit too. I found it really cheaply at Windsor Horse Show a few years ago and have never seen another one. The Premier Equine waffle coolers look similar (in photos at least) though. https://www.premierequine.co.uk/buster-waffle-horse-cooler-rug-c2x21443287
I like Thermatex the most for this time of year or when clipped etc. Although I think its a bit too warm for summer, then I tend to use a waffle type cooler.