If there is adequate ventilation, then the inside and the outside will be at the same temperature. So add ventilation. (Screen the vents as necessary to keep out all intruders.) Ventilation will also help reduce the humidity inside the shed. I would want to add several vents through the roof, and several more down at the base to allow for good air flow.
It is possible no vapor barrier was used below the floor of the shed, which is one reason the interior is so humid. This is something difficult to change now. Of course, if the floor is made of dirt, then I'd add a vapor barrier, then a properly poured floor.
Next, use insulation on the underside of the roof. Spray foam is perfect here. Pick a day to do so when you can dry out the roof, possibly a fan may be necessary.