Apart form any lift effects, the wind pressure on the fuselage and vertical stabilizer (acting at a center some distance above the runway) would create a torque and a weight shift onto the downwind gear. But I doubt this is very significant, and rudder input to prevent weather-cocking would also also offset some of the torque about the longitudinal axis. And unless there was an anti-lock brake release on the upwind gear (unlikely on a dry runway?) it's not clear how it could affect brake temps at all.