While it's true that a metal roof will absorb heat when directly exposed to the sun, the same is true of any roof covering material. A dark colored roof in either asphalt, ceramic, slate or any other material will absorb heat at roughly the same rate.
A roof is the top covering of a building, including all materials and constructions necessary to support it on the walls of the building or on uprights; it provides protection against rain, snow, sunlight, extremes of temperature, and wind. A roof is part of the building envelope.
Puncture the ceiling with a screwdriver to drain the leak.This will cause the water to drain from the ceiling and can help relieve additional water damage. Keep the bucket under the water damaged ceiling so that it can catch the water when you puncture it.