If I were you I would at least rule out some sort of thyroid dysfunction. Beyond that, I am not sure what other medical conditions could cause this, although I am certain there are others.

Psychologically, yes you can react differently to hot and cold than 'normal'. Your body temp being low like that upon waking up in the morning could signal something else is going on. Idk.

I get hot easily when I am anxious. When I am depressed I am more numb to any heat or cold sensation. My body will react normally.. like I will sweat for example.. but I don't feel noticably hot or cold while everyone around me does and I know I normally would.