Suzan, I had the same problem, a conservatory that was impossibly hot when the sun came out, we had to rush to open the windows and doors, it was so hot we couldn't be in the room, when it rained the noise was incredible..... and we have a lot of rain.
Solution, fitted a solid roof with 8 inches of polyurethane foam between and below the joists, oriented t&g glued strand board, covered with geotextile material topped by a Firestone rubber one piece roof and one to two inches of pea gravel.
Result, all year round use, heating costs below half, total silence when its pouring with rain, heaven..