Frozen my beer during cold crash, was the thermowell the isssue?

A week or so ago I brewed my first beer with the anvil fermenter. It's also my first try using a thermowell. I thought I was a genius for sticking a bung thermowell in place of the stock one it came with. Everything was smooth, temputure control was perfect. Maybe off by 1 degree the entire time. Only until the cold crash I had an issue. I had a starter for my next batch on top of my fermentation chamber, so I didn't have a chance to look inside for a few days. I noticed that the temp read 36F and thought that was weird so I popped it open only to find this. I had it set at 33 degrees and figured that would be okay. I'm honestly not too concerned about the beer. I'm letting it thaw and will keg it tomorrow.

What I would like to know is how can I avoid this again? Should I set the temp higher? Maybe 35? I know that the freezer is getting colder than the beer, but I didn't think it was that drastic. Should I pull the probe out higher so it's in the ambient temp of the fermenter instead of the liquid? Any help moving forward would be appreciated.