After it has been out of stock for a while, B&H just received a new shipment of Nikon D810 DSLRs and they confirmed to me that all cameras in their warehouse already have the fix for the thermal issue (white dots) during long exposures.
I am curious if those "new" cameras will have a different firmware update. If somebody has purchased one, please share the firmware version in the comments section. Thanks!
Update: it seems that the new D810 shipment has firmware update C 1.01 (before the thermal issue fix, the firmware was C 1.00).