It may be the venlafaxine as it is a common side-effect. Serotonin is not just a brain neurotransmitter. It has many roles in the body including in mediating blood vessel tone, constriction and dilation, and in regulating body temperature through the hypothalamus and these are likely the cause of the excess sweating.
Switching to another AD may resolve the issue, but there are no guarantees as it is a potential side-effect of all ADs. It seems to occur slightly more often with paroxetine (Paxil) and sertraline (Zoloft) so I don't recommend switching to these. The SSRI least likely to trigger it is fluvoxamine (Luvox), however, as with everything about ADs, YMMV.
Small 1mg doses of the blood pressure medication terazosin (Hytrin) have
been shown to significantly reduce SSRI induced sweating, as have
oxybutynin (Ditropan) which is prescribed for overactive bladders and the
antihistamine cyproheptadine (Periactin), but I suspect many GPs would be reluctant to prescribe them. They might consider gabapentin, however, which is sometimes prescribed for menopausal hot flushes and night sweats. It might also be worth first discussing this with your pharmacist as there may be an effective topical preparation.