Lanai heating and cooling

I bought a condo down south that has a lanai this past winter.  The main patio is technically indoors. However,  you can go through a sliding door to the lanai and it is completely sealed inside with large glass windows. The lanai is super cold all year and I am planning on turning it into a workout room right away. It is literally perfect. The length, width and height are just right to hold numerous gymnastic mats and other workout items. I like tumbling and that is what I do for exercise when I do it. I could do my moves, while seeing the neat outdoors. The only complication is that the windows are not great for temperature control at all. In the early summer the sunshine through the windows will be intense, I am told. Also, the chilly hot and cold temperatures will seep into the windows fast and make the workout section seem colder. So I have been thinking about installing a heating and cooling proposal just for the lanai now. I recognize I am going to get a ductless heat pump system if I am lucky to do so. The heat pump is both heating and cooling, while it runs with heat energy.  And even so, down south it does not get too cold that the heat pump can use the heat energy in the outside air no matter what the season. This method of heating and a/c saves me a good amount of money. Also the heat pump is small and can be mounted on a wall in my workout room, no HVAC duct is needed so the room loses no space. I can even get a smart temperature control for the component so I can run it from my cellphone, which is really amazing! This will be so nice once everything is installed and all set up right.

heat pump device