SLOBRA, I have a 2011 FE570S and have the same problem. To date I have wrapped the exhaust mid-pipe, put reflective material on the underside of the tank, and replaced the factory exhaust can with an FMF unit. It still stalls after 20 to 30 minutes of easy riding in moderate ambient temperatures. I am convinced that the problem is the fuel pump, and have a CA Cycleworks replacement on order.
2011 FE570S: de-smogged; Husaberg rear brake disk guard and low seat; FMF 4.1 Factory slip-on muffler; System Tech Racing speed bleed fork valves, rear caliper radiator, and brake pedal; home built exhaust guards; Pivot Pegz.