How long it takes to cool a planet?
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)