Ours faces west, with one side facing south. It does get hot in there, but is fine once opened up; it has double doors and top opening windows all round. It also has a Solaroof which reduces the heat and glare, and vents (manual ones) in the roof and around just under the roof.
We had underfloor heating installed which is not enough in the depths of winter but takes the chill off in spring/autumn, but also use an oil-filled radiator which warmed it up nicely even when there was snow outside. We are very pleased that we have been able to use it all year round, unless, of course, it is about 30C outside, when we would be looking for a shady spot in the garden anyway.
We have just been away for a week and we shut all the blinds before we went and I moved my houseplants inside into a cool room before we went. The blinds are vertical blinds (not as expensive as some) so we can open them fully, 'slant' them or close completely.
Perhaps the roof panels could be replaced with anti-glare panels which would still let light in, Nfk? It could be a cheaper option than a proper roof.