Earth's atmosphere is 10.33 tons of N2/O2/Ar (plus tiny traces) for every square metre. At the top it radiates at an effective temperature of 255 K to balance the Sun's heat that's absorbed. That means a heat-loss rate of 240 W over every square metre of planet. At that temperature the emissivity is roughly the same all over the planet, close to 1, so it would radiate pretty evenly. Of course currently, in the Sun's shining, net heat-loss is from the upper parts of both hemispheres, while net heat gain is in the tropics. Without the Sun there's quite a lot of stored energy in the oceans to redistribute before everything starts freezing out.
Let's assume the atmosphere is on average at 260 K and it's radiating at 240 W. Each kg of air stores 1003 J/K over the temperature range in question, so there's ~2.7 GJ to radiate away at 240 W over every square metre. Thus ~11.2 mega-seconds, 130 days, to absolute zero. In reality the radiative power declines 1/T^4, so the air at 127.5 K is radiating just 1/16th of what it does at 255 K. To get from 255 to 127.5 K takes (2^3-1) times 130 days - 910 days. Roughly the same period again to drop to the condensation temperature of N2 at ~63 K. Past that point the equilibrium temperature of the Earth from its geothermal heat is ~33 K, and that's how cold the Earth will ultimately get.
But this neglects the heat from the oceans. What would happen, taking that into account, would be a net flow of warm air away from the oceans and cold air flowing towards them. The continental interiors would drop rapidly to ~250 K (-23 C or -9.4 F) and then remain there for as long as ocean heat could keep them "warm". As there's 4200 J stored in every kg of ocean for every K that could be for quite some time. There's much, much more heat in the oceans than there is in the atmosphere. A net flow of moisture, condensing out as snow and frost, will slowly create glaciers on the continents until the tops of the oceans freeze over and the ocean ice tops become as cold as the glaciers on land. That will take some time. A rough estimate would be to equate the energy difference stored in the oceans (which average 5 C temperature) with condensed water ice at ~250 K. The ocean water mass spread over the whole planet would be 2640 metres. Ice holds ~2 kJ/kg.K, energy of freezing (fusion) is 334 kJ/kg and 21 kJ/kg is stored as heat in 5 C water. Thus about 500 metres of glacial ice condensed from gas phase (2.3 MJ/kg) is the equivalent to the stored energy difference in the oceans. As the continental area is ~1/2 the oceans - accounting for exposure of the shelves as sea level drops - that means about 1 km of ice will eventually blanket the continents.
How long that'll take is probably ~centuries since all the heat released must trickle away at ~230 W from the top of the atmosphere to space. The slow decline to the liquefying and freezing of the N2/O2 will take a few millennia beyond that.