i had a similar problem, the insulation on the fire way was all wet and dripping on the exhaust. thought it was the heater core, but turned out to be a bad heater hose, it was leaking at the core tube, but was leaking down the wall and dripping out the bottom, top of the fire wall was dry. bottom was soaked.

my wind shield was fogging up so thats why i thought core till i found the hose was all fvcked up at the end of the hose.