Is it worth putting a one foot high window to capture southern solar heat?

The size and shape of windows makes a big difference for designing a passive solar home for collecting heat from the sun. A high quality south facing window will be able to collect more heat when the sun is up than it will lose at night, albeit with a few caveats.

To maximize heat gains you would want triple pane windows, or suspended film windows for even higher R values, and windows should have low E coating and preferably be gas-filled. Here is a page that explains what to look for - 

Tips for what to look for when choosing high quality windows

Another big variable that determines if there will be a net heat gain through south facing windows or not is the glazing to frame ratio. Due to increased heat loss through framing members compared to insulated walls, the shape is very important. Meaning – at only 1 foot high and 15 feet long, you have 15 square feet of glazing but 32 feet of rough opening with increased heat loss. Compare that to a 3x5 window for example which also has 15 square feet of glazing but only 16 feet of rough opening. They will have the same added gains but very different losses, so a 3x5 window may have a net heat gain but a 1x15 window may have a net heat loss. Having said that, there is more at stake- The other variable with south facing windows, which is not measured in energy consumption, is quality of life. 

Natural lighting in a home has huge mental health benefits, so whether or not you will gain heat from that window, also consider the benefits of sunlight streaming into your home not just for heat gain, but in terms of enjoying your home. You would even save a few bucks in lighting, but mostly you will probably enjoy your home more and that is an invaluable factor in home design. 

Here is our DIY passive solar home design video series, there are some tips in there that may also help.   

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