Just saw this, too late for this time, but it might help next time.
Yes, you should let the cake cool uncovered. But for situations like this one, sealing the cake with a simple syrup or apricot glaze crumbcoat is perfect. This is actually why I started using the thinned down apricot glaze to crumbcoat.
I can buy the glaze ready made and I measure it and add 1/2 that amount in water. So for two cups glaze, add 1 cup water. Bring to a boil and boil for 3-5 minutes. Remove from heat, measure out about 1/4 cup which will cover most cakes. Brush on while hot onto your cakes as soon as they come out of the pan if you like, or you can brush hot glaze on a cooled cake. Let cake cool until room temperature. You can leave a cake sealed like this up to about overnight before frosting.
Otherwise, use pure apricot jam. Bring jam to a boil, over about medium low heat and boil for about 5 minutes, stirring off and on. Press through a sieve to get rid of pulp. Measure and add half this amount in water, so 2 cups heated strained jam to 1 cup water. Return to a boil for about 3-5 minutes. Ready to use.
By thinning with water, you will not get the taste of the apricots. Otherwise you can just heat the ready-made glaze or jam without the additional water.
Brush very sparingly on a cake, just enough to get a sheen, not enough to soak a cake. 1/4 cup will do a ten inch round or bigger, you don't use much.
Store glaze for months in the refridgerator, removing what you need and heating it in the microwave in a custard type glass cup.
Hugs Squirrelly Cakes