I am on Effexor XL and with my last dose increase I found out perspiring is a side effect. You could be getting double whammy side effects one from the med and one for menopause.
Once my body adjusted to my last increase of the Effexor the perspiring is very infrequent now. I sleep with my ceiling fan on medium every night as well as the window at the head of my bed cracked a bit.
I went through menopause without a single hot flash or breaking out in a sweat. God must have been sparing me from that as he had bigger challenges for me.