We were just there May 25th to June 1st. It was thick at times, but it was more than manageable. Hardest thing was finding a place to sit at Cosmic Ray's. Don't know why I even went in there knowing how crazy it usually is, but we never waited more than 30 minutes for anything we rode standby and those were for Buzz Lightyear and Journey Under the Sea which we had fast passes for but wanted to repeat. I'm sure you will find it busy if you are used to January, but it was fine for us. Probably our best trip yet.
It was hot, but we had fans and plenty of water and we managed our time in and out of the air conditioning. And we had just the normal afternoon rain when it did rain and loved it after we had named Tropical Storms on our last two June trips. If I had the opportunity I would choose that week again no problem.