One warm and one cold hand when running

[IgorCvetkovski]

It's nothing to worry about, it simply means that your left hand has worse circulation than the right so your right hand has a steady blood flow allowing the body temperature to remain neutral while your left hand is lacking that steady blood flow so the temperature goes down. This is quite normal, especially in winter. This is the same reason why a lot of times your hands and feet will get cold even when under a blanket.