The volume of the Earth ocean is about 1.37
billion km^3
http://hypertextbook.com/facts/2001/SyedQadri.shtml

A km cube of freshwater is about 1 billion tonnes, so there is more than 1.37 billion billion tonnes of sea water.

It requires 4,186 Joules to heat 1 kg of water by 1 C.
It requires 4.186 million Joules to heat a tonne of water by 1 C.
It requires 1.37 times 4.186 million billion billion joules to heat the ocean by 1 C.
Or:
5.73482 x 10^24 joules

"For the whole Earth, with a cross section of 127,400,000 km², the total energy rate is 1.740×10^17 W, plus or minus 3.5%. This 174 PW is the total rate of solar energy received by the planet; about half, 89 PW, reaches the earth's surface."
http://en.wikipedia.org/wiki/World_energy_resources_and_consumption

So, according to wiki: 8.9^16 W
In a year: 2.8 x 10^24 Joules

"The total solar energy absorbed by Earth's atmosphere, oceans and land masses is approximately 3,850,000 exajoules".
http://en.wikipedia.org/wiki/Solar_power
Exajoule: 10^18 J
So, 3.85 x 10^24 J

If the ocean absorbed 1/2 of the sun's energy which gets to surface per year:
1.4 x 10^24 Joules
It would require a few years for the Sun to warm the ocean by 1 C.

If you remove the Sun how long does it take to lose 1 C in ocean temperature?
If you assume it's absorbing 1.4 x 10^24 Joules per year and losing 1.4 x 10^24 Joules per year thereby not getting warmer or cooler. Then if you remove the sun, the ocean should not lose more energy than it's was losing and maintaining it's temperature- it should lose significantly less in terms of yearly energy loss.
So that means it will take a few years for the entire ocean cool by 1 C with no sunlight.
The land and the atmosphere are completely different- they would lose more than 1 C is less than an hour or so of no sunlight. In days the land and air will lose more than tens of degrees.
So days after the disappearance of the Sun the cold air will cool the ocean surface. But as you noted in terms of mass, the air insignificant in comparison to the Ocean's mass- and so won't have much affect upon the entire ocean temperature.
The land surface temperature will cool rapidly, but a foot or more below the surface, temperature could remain above freezing for months.
The ocean water which is cooled by cold air will sink to be replaced with warmer water. As long as ocean doesn't freeze- which could take years, the atmosphere will not become a cryogenic liquid, but it will collapse into denser and become a smaller atmosphere- perhaps having a Mars density atmosphere at 20,000 to 30,000' instead of 100,000'.

If the Sun returns in about a year, the ocean temperature won't be affected much by it's return, the atmosphere will response quickly and warm the most, and land surface temperature will start to warm significantly once air temperature are warmed up, and ground temperature below a foot requiring the most amount time to recover their temperature to levels prior to the Sun disappearance.

Now, one result of this is that there could be decades of time before polar sea ice is created- each year you will have less polar sea ice than the year before, but because the polar ice could have made quite thick it won't melt during the summer, nor will much ice be added during the winter- because the insulating affect of the existing ice.
So the polar ice pack will slowing retreat.
This could stop the global conveyor belt which cools the tropical and temperate oceans.
Therefore it's possible the the result could an increase in global ocean temperature for decades or centuries after the sun returns.