Have a look at any back pack with a ‘suspension’ system to lift the majority of the pack from your back.
Brands that spring to mind are Vaude, Deuter & Osprey.
I’ve got a Vaude Splash Air 20+5 and have used it for commuting. It stashed all the kit I needed, although I didn’t have a laptop and I kept toiletries at work. The back arch is quite pronounced, so it can make loading it a bit tricky, but it does keep your back a lot cooler and stops you getting poked in the back with stuff in your pack.
The straps are well padded and adjustable for body size, so it’s a very comfortable pack.
My only grip with it would be that it doesn’t have enough pockets for organising stuff, but that shouldn’t be a problem for commuting kit.
If you need to get a laptop in there too, perhaps go for a bigger version.
I’ve also got an Osprey Syncro which would be way too small, but just to mention it; the arch in the back is a lot more subtle than the Vaude version so a suitably sized Osprey may be more appropriate.