I guess you are referring to extreme heat in the summer and the reverse in the winter.
In the summer, clearly orientation is critical but you can't do anything about that now. You have to stop the sun rays penetrating inside and blinds (vertical plus angled over the roof) is really the only way. Mediterranean countries use shutters on the outside (on their dwellings) - these look good on houses but probably impractical on conservatories.
In the winter, if you have single glass, 90% of any heat you put in there is going straight up and through the angled roof. So you have to address that. Modern glass structures will have double and even triple glazed panels but these are extremely heavy and retrofitting is expensive and the rafters are unlikely to support the extra weight - they have to be designed for it. You may be able to change the panels for translucent polycarbonate which is now available in quin-wall (four air gaps) to prevent heat loss. This would be a complex but not impossible DIY job. Any lightweight, temporary insulation you put up at the start of winter as an alternative is going to make the roof panels opaque, and hence the room dark.
No easy and cheap solutions I'm afraid - its an inherent weakness in the design. There no such thing as non-opaque insulation (well there is - its called air gaps).