Will fridge condensation ruin old labels?

Right now in my basement, the temps are ~75F during the day and ~70F at night. I decided this was a bit hot, so I moved some of my most prized beers to my mini fridge and turned it on the lowest setting. It's been right around 60 degrees. It's also been quite humid, and it appears that the beers are having a lot of condensation on them in the fridge. I have some really old beers from the late 80's and 90's and I really don't want to ruin their labels. If they get too wet I fear they may get damaged.

I've considered putting them back down in my cellar to let them dry, attempt to thaw out my fridge and dry it out well. I just fear this will happen again in a week if the humidity gets bad again. Has anyone else run into this problem cellaring before? What is the best course of action?

Any advice is much appreciated.

 

They've been cellared properly up until now to the best of my knowledge. What would a larger fridge or freezer with a temp control unit change when it comes to humidity on the inside of it?

Thanks for the advice.