How long it takes to cool a planet? Suppose a planet like Earth or Venus is totally isolated from sunlight. How quick would it cool down?

On Earth it seems to me that the air temperature drops significantly even during a night. Does it mean that if we screen Venus of Sun's radiation with some untransparent cloud, it would cool down rather quickly, and not for millions of years as some may expect?
Not a full answer as that is hard to give.  But:

This is a diagram by Kevin Trenberth picturing energy flows in the Earth climate system:


(Source: Skeptical Science)

In the hypothetical extreme case of blocking all incoming solar radiation, the Earth would — initially — have a net heat loss of roughly 340 $W m^{-2}$.

93% of net radiation change on Earth enters the oceans.  In the past 20 years, this has led to an increase in ocean heat content (OHC) of roughly $10^{23}$ J.  With a 340 W m^{-2} heat loss, undoing that would take $10^{23} J / ((340 W/m^2) * .7 * 510 * 10^6 km^2$ which is roughly 10 days.  Although this is a severe oversimplification, it does give us a first order of magnitude.

It might be possible to run a climate model and switch off the Sun, just for fun.  You don't need a heavy climate model to do so.  PlaSim is good enough to get a handle on it.

My guesstimate is that it would take a couple of months before mid-latitude oceans start to freeze.


(Source: EPA)