Metal roof leaking

Hello all. In installed a metal roof about four months ago over an existing shingled roof with fir straps 24" on center. On two occasions now the roof has leaked. The first time was when we got our first dusting of snow last month. Today was the second time. It's been below freezing for the last week or so and today it's around 40. The room where it leaks has a cathedral ceiling with 2 x 8 rafters so there is 7" max for insulation. I am thinking the heat loss is escaping and hitting the back of the freezing metal creating a lot of frost and when it warms above freezing like today it drips creating a leak in the house. Do you agree or am I missing something? The first leak was on one side of the room. Today it is two spots on the other side of the room opposite side of the roof. There are no pipes or anything protruding through the roof in this room.

A metal roof with no insulation almost always gets condensation on the inside in my experience. It doesn't need a lot of insulation to stop it, my friend has just put maybe 1/2" polystyrene inside the roof of her shed and there's no problem any more.