The pump may not be any hotter than usual -- you may not have checked before.
But, the hesitation on start often indicates some mechanical aspect of motor and impeller is not turning freely. There can be a couple of causes, but in my experience by far the most common cause is worn bearings.
A weak start winding or start capacitor (may not have either -- don't know what motor you have) could also cause a slow start, but usually it would be slowly, the same way every time.
Motors can be rebuilt, but replacing the motor is a 'cleaner' fix if you can do it. Also you may not have a rebuilder in your area. If you get a new motor, be sure to also get a new seal and any new gaskets / bushings / washer that are long the path of the motor shaft.
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