Let's crunch a few numbers.
As Anders observes, "The heat capacity of iron at room temperature is 0.444 J/K per gram (it changes with temperature, but let us leave that aside)."
So your entire mass needs to absorb 4440 joules per degree K it rises. Just getting that to 273K (freezing) will call for (coarsely) 1212120 joules.
Water has the impressive 4.18 joules per gram per degree C of heat capacity. Its enthalpy of vaporization is 2265 J/g which means it must give up that much energy simply to liquefy. Its enthalpy of fusion (freezing) is 334 J/g. So that's 2599 J/g water vapor must give up to freeze, plus another 26.85x4.18 = 112 J/g to cool from 300K to freezing, totalling 2711 J/g.
Why am I talking about water?
Because water will be doing all the heavy lifting here. After all, water and its potent enthalpies moderate the temperature of this planet!
How many grams of water vapor must freeze to bring the block to freezing? 1212120 J / (2711 J/g) = 447 grams.
Almost exactly 1 pound of water. I should've used British Thermal Units!
Is that even in the room? Well, if the air was 27C and at 100% relative humidity, it would contain 27 g per cubic meter. 16.5 cubic meters would hold that much water. Say we're at 50% RH, 33 cubic meters, that's a rather modest bedroom! So the room surely has enough water to do the entire job.
The sequence of events
Yes, instantaneously, it will freeze the nitrogen and oxygen. But very quickly, that will re-vaporize as it exchanges heat energy with water vapor, which eagerly freezes in its place.
This ice will act as an insulating layer to slow heat transmission further. It will expand and expand. Though it won't be terribly thick: after all, we're dealing with less than a pint/half litre of water. 1 water bottle.
Eventually, this will slow down. Even before the iron core has reached 273K, water on the outside will start being melted by the heat in the room, either convecting from objects in the room, or the thermostat has switched on and made a call for heat.
In room air conditioned to 27C, it is easier for water to gather the 334 J/g needed to melt than the 2265 J/g needed to boil, so once the water has melted, it infuses into the (now dry) air much more slowly.