Several times this summer while riding in hot weather at low speeds all the electric (engine, lights, starter, ...) dropped out and everything came to a halt. Each time I'd turn the key off and back on, hit the starter and it started back up and ran for a while. The last time this happened I turned the lights off after restarting and it ran OK until I turned the lights back on, and then the electric dropped out after a while. I noticed the engine got VERY hot before the electric dropped out, but the oil cooler fan and hot indicator lamp never came on. When I disconnected the thermistor, both the fan and hot indicator lamp come on. Any ideas on what might be the problem?

 

Sounds like the old ecm problem and recall that didn't include your model,but should have. Ecms can cause all sorts of problems,from engine stalling,dieing,not charging back to the battery and some even caught fire.Huge ATV Recall by Polaris - Sportsman and Scrambler
Doesn't show an updated module for your 330 on Polaris Parts Breakdown or other web sites,but you may get an updated one from this part #. Item #18. Dirt Cheap Yamaha, Honda, Arctic Cat & Polaris OEM Parts & Accessories – Cycle Parts Warehouse