In places like the Giant's causeway in Ireland (Antrim basalts) there are columnar basalt flows of 100 metres or more. I'm aware that the cooling mechanism is complex, but is there any rough and ready equation for estimating the cooling time of such a basalt flow?
If you don't want to get involved in the math, you can use one of mane heat transfer simulation software, there are even online version that run in your browser like Energy2D, in which you can configure the geometry and thermal properties of your materials and let the simulation run.
The screenshot below is a problem with the geometry you suggest. But you would need to set the correct thermal properties of air and basalt.
If you are looking for a customized equation, you have to constrain the geometry of the problem. For instance: the cooling of a laterally infinite layer of material at 1000 °C of thickness X with a medium (air in your case) above it, at constant temperature of 10°C and a medium below it (bedrock) at initial temperature 5°C, you can look at engineering formulas handbooks, or post the question on the Engineering or Math Stack Exchange sites.