His latest is here. I am submitting the following as a comment:
1. This conference focuses on theory but Paul Williams' presentation, the second talk on the list, touches on the kind of thing you have in mind. See also Schumacher's talk and perhaps others.
2. I had a similar idea: build a miniature analog of the Earth and include the heat flow from the Sun.
How to scale everything perplexed me, though. For example, the stratosphere extends up to about 30 miles on a planet whose radius is 6000 miles. Not only that, the dynamics within the atmosphere is complex. How do you infer what happens on the Earth from what happens in the scale model (if you can even build it)?
Nevertheless, IMHO suggestions like yours have merit as exploratory research. How well can current scientific models characterize simplified heat transfer environments? If the models work well there, that somewhat enhances confidence wrt their applicability to the Earth. If they don't work well there...