This is your evaporator temperature sensor. It has failed.
What happens is this. The evaporator temp sensor fails; the evaporator ices up; after about 5 or 10 mins it stops working; the cabin heats up; the acc system tries to compensate by increasing the fan speed; eventually the fan is running full speed but no air is coming out.
You can check this yourself by running the diagnostic test from the push button control module. The evap temp sensor is value number 5, it should be about 4 or 5 deg C, if it has failed it will return an illogical value such as 40 deg C. If you use the search facility you will find a raft of posts (many by me) on this topic. Search for "evaporator temperature sensor" in Tech Help and SL Forum.
It is a cheap part (cost me GBP40, probably <$100), and an easy fix (pull the old one out, put the new on in).
Here are some relevant threads (I've done the search for you):
1999 SL 500 Blower Issue - Help Please!
R129 AC problem