Did you ever get this figured out? I have Raynaud's syndrome (concomitant with a lupus-like autoimmune disease) and typically have cold feet most of the time. However, usually half-way through my sessions, my feet warm up. That's just me though and these kinds of conditions are highly individualized. I definitely don't recommend hot water for something like this, regardless of the cause. Blood vessels "shocked" into dilating in that way can just as quickly constrict in response. I have tried starting out in yoga socks when my feet are at their coldest. It's not ideal because my feet slip inside the socks even though the sock doesn't slip on the mat. I've considered trying Vibram Five Finger "shoes" but suspect it would cause a similar problem. If my toes didn't turn blue and go numb, I'd just muddle through. Core temp is the most important thing for me but it isn't the only thing that controls the problem. Certain postures can trigger it as well as well as sudden temperature changes (going from a warm house to a cool or cold outside. Being out on a hot day and getting into an air-conditioned house or car).
I hope you've got it figured out.