Hi and welcome,
The answer is that yes a lesion in specific locations (eg hypothalamic lesions) can cause someone with MS difficulty maintaining their body temperature, either getting too hot or too cold but unfortunately it's still not clearly understood whats going on yet...
"In patients with MS, dysregulation of the autonomic nervous system may present with various clinical symptoms including sweating abnormalities, urinary dysfunction, orthostatic dysregulation, gastrointestinal symptoms, and sexual dysfunction."
https://www.ncbi.nlm.nih.gov/pubmed/26213927
It's recommended you speak to your neurologist, there maybe something that you can try that might help, id also recommend you read the self help tips and tricks mentioned on any of the MS society type informational sites.
Hope that helps.......JJ