Is this normal - Electrical outlet - make hot prong on cable a tiny bit warm
Yes, that's normal especially when running a relatively high-powered appliance like a vacuum.
As long as it's just &quot;warm&quot; there should be no issues although sometimes the outlets get worn and the pins inside no longer make good contact.  It this is an older or heavily used outlet, you might consider replacing it.  This could be why you are seeing only ONE pin getting warm, one may be weaker than the other at this point.
Also make sure the cord is in good condition with no kinks or worn areas.  The vacuum itself can also be an issue if the motor is having trouble due to blockages or bad bearings.
But unless things are getting &quot;hot&quot; you should be ok.