Motor Burnout

When climbing long steep hills I'm reluctant to put it in turbo because I'm afraid of burning out the motor, especially on hot days. Is this a realistic fear? I once had a bike that would shut down if I left it too long on turbo while climbing hills. Thanks
 
The specifics...it was a 2016 Easy Motion with Dapu hub motor, 350 watts I believe. It had no throttle and had 4 assist levels.
 
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