Making the lanai useable-ductless HVAC

I have an attached lanai that is all screened.

This should be an awesome room in the house. Instead it is a hot, sticky mess. The screens let in all the muggy, warm air in the summer. Closing the screens makes it hotter when the sunshine comes in. In the winter the cold seems to linger there. The space is basically unusable. It is wide, long and has a great view. I would love the lanai to be a work out room or at least hang out space for my family. I need to find some way to have superior climate control. Eventually I think I will need to take out the windows. I could get new, all glass windows to make the view better. I then will know the space is airtight. I can install a ductless mini split without any air leaking outdoors. The mini split can provide both heating and cooling and only work in that one space. I could have superior cooling when the hot sunshine comes through the windows in the summer. I then could change it to quality heating when the winter cold comes in. The space could be used all year with good HVAC equipment. I don’t think it will be too expensive after the initial HVAC installation. Anytime I use the space I will turn the HVAC on. When not in use, I can simply power it down and let it be hot or freezing cold. A smart thermostat would make it so I don’t even have to walk in the room to do it too.

HVAC installation