Notice that Ben's arm was already injured when he awoke in the desert. That suggests that perhaps he was in danger, and used the 'magic box' to escape from whoever had injured him on the island. Perhaps they hadn't perfected the technology since the Orchid Video mishap (Ben did kill the scientists working on it, after all), and so it's still unpredictable. Perhaps there was a chance that it could've sent him to the Antarctic portal, hence the warm coat. On the other hand, the Sahara does get below freezing at night.
Obviously Iraq is many thousands of miles from Tunisia/the Sahara desert. Clearly Ben travelled (by horse) from the interior desert to a coastal city, where he has assets in place (i.e. the desk clerk recognizing Dean Moriarty), and travelled by more conventional means to enlist Sayid in Iraq.