Economical solar power
OR
Economical passive heating and cooling systems
The key here is the leading term economical. It is not enough to develop the technology--especially not in simply a proof of concept form. We are interested in when we can truly use these technologies. In some limited cases we are already there for both types, but those are indeed limited. The essence of this puzzle is when can we expect to see these things widespread including in average households. And while these are related in many cases, I don't think I'm splitting hairs here to make the distinction.
A passive heating and cooling system (or either one alone to satisfy the achievement) would be something akin to geothermal but not necessarily limited to such. The roof and attic of my house are exceptionally hot in the summer. Once the sun goes down, my attic cools a lot faster than my garage because the soffits work air through the attic accelerating cooling. There is an opportunity in this greenhouse effect. Similarly, my brother's basement has a more moderate climate (albeit more humid) than the ground floor and upstairs of his house. To qualify a passive system would rely on a minimal amount of catalytic energy to initiate a system that would use these energy properties to the effect of a desired cooling or heating result. To be clear, using my attic heat in the summer to run a generator to cool my house counts.
Solar is the great, green hope. The power the sun rains down on us continually during the day, which is obviously a big impediment to solar energy, is fountain of youth and El Dorado all rolled into one. The future society that can economically use this energy will be quite rich. It is important to note that the there is a bit of chicken and egg here as the society may be rich enough to develop the technology as much so as the technology makes that society rich.
The trends in the economics of geothermal look less favorable as compared to solar (note: the links here are not supposed to be a comprehensive look at the economic trends affecting these technologies). Geothermal capital costs are exceptionally high since the target tends to be on the large scale as opposed to the household level. In the larger consideration of all passive-type, non-solar solutions, many of those potential technologies probably fall into the category of those in need of a happy accident (we aren't specifically looking for these breakthroughs). Because solar is thought of and more so developed for the individual end user, that probably gives it the edge in this WWCF. The other leading factor is that solar is a more politically attractive cause resulting in a lot more "investment" using the best kind of money, OPM.
My guess is that solar edges out passive systems by less than a decade, but both are 30+ years away. The standard error is large in these estimates; so I have very little confidence in my guess about solar winning. I'm sure others have a firmer grip on this, and I will follow up with new information as I discover it.