I don't think there is anything wrong with his manual transmission, nor do I think warming up the car makes any difference. My Mirage doesn't shift differently when cold, & I have done some -20F shifting. It's probably the best cold weather manual, I have driven. I can sense a slight difference with my Subaru Forester manual during the extreme cold.
My Dad's old Farmall H tractor (mighty thick transmission oil that may be 70+ years old) may require two hands to shift when it's that cold. By comparison, shifting the Mirage in the cold is nothing. I really don't notice any difference.