Since getting PD I've been less able to deal with cold temperatures. I get the whole body shivers that you describe if I get too cold.

I suspect that this is fairly common amongst PwP. Hood and Amir write [1]:

"The human core body temperature rhythm rises throughout the day to peak in the early evening, then falls throughout the night to reach its nadir in the early morning ... In PD, only the amplitude of the rhythm appears to be decreased. This change is attributed to a lowering of peak body temperature relative to healthy age-matched controls."

Reference

[1] "Neurodegeneration and the Circadian Clock"
Suzanne Hood1 and Shimon Amir
Front Aging Neurosci. 2017; 9: 170.
Neurodegeneration and the Circadian Clock

John