2010 650 outlander fuel problem ????

Hello guys. I got a problem with my bike. I went bird hunting 3 times this year and all 3 times it acted up. So i was driving at low speed around 10 km/h. After doing between 25 and 35 km on the trail the bike is really hot under the seat. The latch for the seat get so hot i cant even touch it. And when it gets hot i get trottle problems. I get no response from the trottle. Its good for maybe 10-15 seconds and then sometimes it picks up again and if not the bike shuts off. Sometime i have trouble starting it back up and then same thing. Trottle works for a couple seconds then quits. Sometimes while jerking it it picks up again brought it to my dealer here and they couldn’t find anything wrong. No limp mode on screen either. I read here it might be the fuel pump but without being 100 % on that i don’t want to change it cause they want 400$ for a new one.

Thank guys