Hi Rob
I would think that a cold sax is always going to have this sort of problem of condensation when warm damp breath is blown through it,I know you are saying that it is still doing it even though it's warmer now but is your sax kept in a cool place when not in use, I would think that if so, it will take a while to warm up and so reduce the problem.Then there might be the problem of your own metabolism and your general liquid intake may make a difference,and if you tend to be very hot bodied,I would think that it will all make a difference to the mosture in the air you are exhaling,and also the general humidity on the day
I tend to have varying amounts of condensation when I play,and thats on a sax that is left out on a stand all the time so is at room temp,some times I get a ring of moisture round where the mpc fits on to the neck which causes a burble when playing,and sometimes there is a small pool in the bow and other times like you it comes out through the tone holes I think it's probably the usual thing with instruments that get blown...john