In my opinion, the chart in a bar chart works for its intended purpose. However, the chart may not be as intuitive as the dual radial chart being used for the Weather Browser. Time can be told easily in a circle like a clock face. , The chart in a bar chart probably can be used for anything applicable rather than just time and weather. It may also be inaccurate to call it a bar chart in this case considering that a day has only 24 hours, so it means the length of each bar will not differ. Perhaps, something similar is a combination chart that has been used by the Economist that puts together a warming stripe (colour gradient) and line chart.
This post is purely about the experiment than a full-fledged tutorial for creating the charts in Tableau that I have done previously. With that being said, for anyone who wants to replicate the viz, it is done using Dual Axis with "Aggregate Axis" off. You can also download a copy of the Tableau workbook of the Tableau Public by clicking on the picture before the opening paragraph.
All in all, this is an interesting take for me. Instead of the standard bar chart being transformed into a radial chart, this chart is motivated by turning a radial chart back into a bar chart type. With the chart working as an experiment, the real test will be to apply it to other kinds of data. We will then be able to see if it can be truly used as a bar chart.