This is a great question relating to what I believe is a fundamental part of ME/CFS pathology, we're stuck in a thermogenic response. I think I shivered in the early stage of the disease to cold exposure, but not since. I would suggest this is mostly due to extreme cold intolerance I've avoided cold exposure and always clothed for an Antarctic exploration. I regularly wore my Canada Goose jacket indoors during winter, even though in NZ it rarely falls below 0, but now I employ underfloor heating. I really struggle in temperatures below 17 degC.
I've been studying the thermogenic response. Other than shivering, there is also brown adipose tissue and beige or 'browning' of adipose tissue. This is a metabolic adaptation to generate heat by futile cycles wasting enormous energy, not only in Cori, glycolytic and gluconeogenesis cycles but even in the mitochondria allowing upregulation of the ETC with UCP-1 induced proton leak which could perhaps explain Fisher's study (apparently it occurs in immune cells too).
Cold exposure and thermogenic response also involves peripheral sympathetic vasoconstriction to minimize blood temperature loss. I'm sure this is part of the ME/CFS story along with dysautonomia that causes the cold limbs. I do find after I hot evening bath I sleep better and certainly feel more rested the next day. Cold exposure is known to upregulate the thermogenic response, I would assume the opposite is also true, and I believe the heat exposure from the hot bath is down-regulating the thermogenic energy loss. So it doesn't surprise me to hear those who have shivered suffer PEM.
Severe burns patients can endure years of thermogenic response, this is understandable with the loss of thermal barrier. In sepsis it's considerably shorter. So I've wondered why are we PwME stuck in this thermogenic response? I am well into exploring a theory that might be to do with heme sustained thermogenesis, but also involving HPA-axis, as thermogenesis is centrally managed at the hypothalamus.