It's probably not the exhaust. If your muffler is like mine, the outlets open to the front of the machine horizontally. The problem you have, and so do I, is the cooling air. If you stick your head under the front end and look up, you will see the cylinders' cooling fins through the air exhaust side. They point straight down. In fact, the design is so stupid on my mower (YTH24V42LS) that it heats the axle so hot that the plastic covers over the spindles soften and fall off. Both of them that were on my mower have fallen off and gotten lost.
I've been looking at that for a while now thinking about fabricating a shield to redirect the hot air forward like the exhaust. You could mount a shield on the same bolts that hold that useless "brush guard".
Burning the grass is unacceptable IMO. I would think that Husq ought to know that. They even mention it in the owner's manual -- browning of grass can be expected, ignore it. Some solution, huh?