OK- this makes more sense. The condition of foraminal stenosis of C5-6 (see website for this) would cause compression of the C6 nerve. This radiates pain and paresthesias (pins and needles) down to the thumb side of the hand. Weakness would include biceps (bending the arm at the elbow), wrist extensor (lifting the wrist up opposite side of the palm)- important for grip strength and the thumb muscle.
Foraminal stenosis would become worse with neck extension (bending the head backwards) making the radiating symptoms worse. Temperature is governed by the sympathetic nervous system that does not originate from the neck so the coldness in the hand is not related to the neck.
You could also have carpel tunnel syndrome- very common with using a mouse. I do not have a section written on that so you will have to look it up on the internet.