I just bought this well used 400 and fixed the broken front suspension. Ran it up and down the road here and ran fine and no problems. Took it to the trail today and it was hot. It was high 80s for sure. At slow speed it over heats and over half throttle it runs out of gas in a mile or so. I replaced the fuel filter but no help. I havent looked at it much but cooling fan was not kicking on. Anything common? Is there a screen in the fuel tank that could be restricted?

 

Electric fan, and known for the bearing to go out in it, needs to replace, as for the Gas check the fuel pump diaphram

 

The fan can be dissembled and cleaned. that's all that mine needed. there are no ball bearings in those older ones. just bushings. the fan motor is crimped together on one end. pry it apart like a paint can. when you get it off you will see what I mean.
Check the needle position in the carb if it's lean in the midrange it adds to overheating. those units can run pretty cool with a half plugged rad in my experience. but make sure it's clean. in those temps it might want the fan, but anything in the 70's the fan might come on once all day. good luck

 

you will have a had time finding a fuel pump on there (there isn't one)
but polaris put the pickup at the front of the tank. so on long up hills under half a tank it can suck the float bowl dry.
check float height and needle n seat
check all the vent lines, if they touched the pipe and melted shut. that could be the problem