Why engines don't melt? The temperatures of internal combustion engines are well above the melting points of the component materials.
For example, temperatures can reach 2200° C whereas the melting point of aluminium is 659°,  of iron is 1530°, of cast iron 1260°,of high carbon steel 1353° etc.
I have read that the reason for this is the phenomenon called "microboiling".
The cooling water boils locally at temperatures below the boiling temperature, and the created steam has higher thermal conductivity  and cools the engine.
What are the reasons behind microboiling?
And why steam has higher thermal conductivity than water? 
 A: It is all a matter of engineering balance, between the water circulating in the radiator circuit of the car, which enfolds the engine and with water-metal contact which takes heat away at a certain rate.

In automobiles and motorcycles with a liquid-cooled internal combustion engine, a radiator is connected to channels running through the engine and cylinder head, through which a liquid (coolant) is pumped. This liquid may be water (in climates where water is unlikely to freeze), but is more commonly a mixture of water and antifreeze in proportions appropriate to the climate

Microboiling are those small bubbles one sees at the bottom of the saucepan before water starts boiling uniformly at 100C. They are removed with the water circulation raising the radiator water's temperature.
If the radiator loses its water the engine seizes up because of loss of lubricating oil and deformations due to heat, long before the melting point is reached, ( as observed by tfb in comments) and is destroyed. If the water boils it would  remain at the same temperature so cannot work as a coolant. Therefore the water circulates to remove the micro boiling points from the surface of the metal to the rest of the reservoir and cool it at the radiator.
The engineering design takes all this into account, to keep the metal surfaces well below melting and at a good temperature for the lubricating oil by the rate of circulation of water around the engine fast enough. With red lights coming up to stop immediately if the water circulation fails ( has happened to my old car and not only once).
Now as far as containers and temperatures, take the temperature of a propane heated  oven, it is at 2800C, but we cook food in the oven at 180C. Do the oven walls melt? Or even the inlet grid?  It is all about rates of heat transfer and  and it depends on the engineering parameters.
A: All very interesting. Of course if you pull down an engine that has had a piston seize from overheating you will see the aluminium has started to melt as the piston expands and is dragged up and down the cylinder bore. Pistons do melt but by the time they start to melt they have expanded to a point where they are so tight in the cylinder bore the loss of energy through  friction stalls the engine. 
More fuel ,more heat, more expansion, loss of cooling , piston heats up, piston expands a few thousands of an inch and seizes. This is very obvious when one piston seizes due to poor combustion (faulty diesel injector) and the other pistons are working overtime to maintain engine speed at full power. Piston starts to melt and then seizes. The engine can tear the piston in half. I have had it happen  and repaired a few. John          
A: I'll venture the guess, that the explanation you read was wrong. What I'd find plausible is: 
liquid mixed with gas has a higher effective thermal capacity - you don't need conductivity since the stuff is pumped through the cooling cycle, right?
What I mean by this: the liquid can receive a lot of heat by boiling. It carries the heat away not only in the form of higher temperature, but in the form of beeing a gas. In the other part of the cycle it can give away a lot of heat by condensing. 
At least this is how heating works in dairy factories where I have been: when pasteurizing the big steel tanks, you pump vapour (with pressure greater than atmospheric, of course) in them, which condenses (therefore pressure drops, and more vapour is sucked in), which heats them very effectively. 
The engineering problem in the cooling system is probably, that it's more difficult to pump such a mixture (like the blood in you veins, when delving upwards from a great depth too fast, might form bubbles and stop flowing, very dangerous). That's why it might be advanatageous, if all the liquid touching the engine gets evaporized, so you have no mixture, only arriving liquid and departing gas. 
That are "educated guesses" which hopefully explain part of the surrounding physics. For a practical explanation of the occuring issues probably engineers are the better audience. 
A: Engine will not be running at 2200 deg for all the time.It only happens at the power stroke at negligible time i.e. it is in such a way that heat is dissipated in fraction of second through Fins and oil.As you said engine is made up of Aluminium, Aluminium has the highest thermal Conductivity.Hence Engine is not melted.
A: Combustion gas temperature can be as high as you quoted. But metal temperature is much lower than its melting temperature. At high temperature, metal will lose its strength. Engine design will not allow this to happen. During the cycle, combustion gas tries to heat up the metal. But there is coolant flow carrying away the heat. The net is that the metal keeps the temperature low. When the coolant system failed somehow, metal will melt. 
A: Air fuel ratio also plays a major role in controlling the peak temperatures attained in an engine.The temperature will be the highest at the stoichiometric ratio because of the complete combustion of higher quantity of fuel.Since the engine operates at very high speeds, complete combustion occurs at a slightly leaner than stoichiometric ratio.But usually this leaner mixture is not used .The engine management system with the help of temperature sensors will optimise the air fuel ratio.
