Habman, the exact thing happened to me. I had 5 trays that were not covered and 3 that were. The three that were covered got a case of "mold" or "fungus". I think the high humidity + heat is what did it since the 5 uncovered trays did not experience the "sickness".
I sprinkled yellow corn meal on the surface and it either slowed it down or killed it. I will know more when I start transplanting to 9 oz cups tomorrow. If the fungus/mold is in the soil I will give it a good coating of corn meal again. This worked for me on my baby nagas. They got a case of the "green" that was visible around the cup/soil interface. When I transplanted them to 6" containers, I mixed cornmeal in the soil and coated the outside of the root/soil mass. The baby nagas are coming on strong now.
Ms. Pam made me a believer.