Hi timmyEGCC,
as more weight means more loads on the wheel bearings therefore more heat being produced...
Er... not so.
The wheel bearings don't generate the heat, the brakes do.
The brake energy absorbed is proportional to the Force * Distance traveled, so if they apply a constant braking force (LO say) the brakes generate heat rapidly during the early part of the landing roll. But this is when the biggest difference between the weight on L & R bogies is felt during a crosswind landing with no aileron applied.
As HazelNuts39 points out, this effect will only happen if the anti skid is releasing the (cooler) wheel brakes. Since the total weight on the wheels is the same (with and without a cross wind), but the aircraft wants to roll in a crosswind (with no aileron applied), then the down wind bogie supports more weight than the upwind bogie. If the required braking force is sufficient to trigger anti skid release on the upwind bogies initially, then you'll notice the difference in temperatures. The overall deceleration will be the same, just the downwind brakes will be working harder.