Welcome Jules,
Sorry you had to come find us but there is a great group for support here. I have not personally had a block so take that into account. However a sympathetic block by nature warms the limb in anybody. So it should theoretically, if they hit it right, warm things for the duration of the block. One PM told me he had one patient whose limb was primarily cold and after the second block that issue resolved. Obviously results will vary. I chose not to get one because I was progressing on my own and overproduce scar tissue pretty much everywhere for any reason.
good luck, I hope you find relief soon.
Sending Healing Love,
Littlepaw