Does "My cold bits" mean "my cold part of the body"?

[NewHopeR]

Context:

The uphill work weaving through traffic, that murderous young mother blindly cutting through the cycle lane … all forgotten. I’m standing here as God made me, old but fit, tired but pleased. My cold bits are warm, my sweaty bits washed. I’m feeling blissfully alive. And, I’m at work. Everybody else, upstairs and downstairs, they’ve all got their clothes on. They were protected in their cars and are now protected in their clothes. They gently pretend and tell only half their truth. But me … I’m wet and warm with my bald head and naked as a babe.

[JMurray]

The parts of the body that got cold as the person was riding the bike to work, are now warm, the sweaty parts are now clean. It seems that the person is having a shower after bicycling to work.

not a teacher