Most of the interesting "weather" and dynamics in the lower atmosphere arise from convection.
I think the link that was posted was mainly about how convection dominates in the lower atmosphere and and radiation effects dominate in the upper atmosphere, and wanted to see what the effect of would be if one artificially looked at the problem without convection. As pointed out in comments and other answers, it is unrealistic to not have convection. The link article by having a thin ocean was mainly trying to set a boundary condition for the model, and if I read it correctly that if the ocean was thick the equilibrium temperature would end up same if you waited long enough. One way to interpret the article is that the convection in the lower atmosphere mixes up the fluid (air) in such a way that the surface doesn't get as hot as it would without having a layer of atmosphere mixing.
From a world building perspective, I think to get at the heart of your question it is about how could you control the temperature of the planet assuming that radiative processes are dominating the heat transfer balance.
The answer I think would be by how much reflectivity (from the surface or perhaps clouds) and emissivity the planet has. From a climate science point of view, this is a big deal. In the air how much to contrails from air traffic change the heat ballance, surprisingly to me, apparently it is measurable. 108
On the ground, or ocean, how much soot from combustion is landing on the snow, or how much ice coverage in the arctic ocean matters in a lot of these models how the light from the sub is trapped or reflected is important.
So for your purposes, you have the light from the sun hitting the planet and the light and heat from the planet radiating into space. Neglecting some details, that the planet may have started out as hot mess of molten rock, and over time new materials from space may be adding water etc. That should come into equilibrium.
A short light article with a graphic is at
https://www.physics-in-a-nutshell.com/article/17/surface-temperature-of-the-earth
The atmosphere acting as a filter as to how to how much of the light and heat from the sun is reflected, how much is transmitted to the surface, and how much of the higher energy photons are absorbed by the gasses in the atmosphere or by the ground and turned into heat (lower energy photons) that would go through the filter and radiate into space.
To dial in the temperature for your world, the easiest thing would be to fiddle how much light is reflected and absorbed. The knobs you can turn (ignoring the convection) would be to add more gasses from volcanoes like CO2 that might absorb and trap heat strongly, but not add a lot of particulates from the volcanos, or clouds in the atmosphere that might reflect more of the light before it gets absorbed. Without CO2, from the volcanos, maybe the oceans are frozen before the eruptions and the earth is very shiny and reflective. Or you could add plants, and they could consume the CO2, and perhaps the plants change the reflectivity of the oceans, or maybe the oxygen from the plants starts to oxidize the land etc.
Volcanoes are not the only thing but just an example of something that can change the heat balance in a short period of time. But basically changing the Albedo of the planet (with or without) a convective atmosphere can change the heat balance and the surface temperature significantly. 184