What condition may cause the plug or the power adapter to become very warm or hot?
An equivalent formula for Olin's is 


  Power = Voltage \$\times\$ Current  


and


  Energy = Power \$\times\$ Time  


All substances have a heat capacity, which indicates how much temperature rises if you add a certain amount of energy it. For instance, if you dissipate 10 W during 1 second temperature may rise by 1°C. Another second and it rises by another degree. So you would think temperature will keep rising as long as you use the adapter, but fortunately that's not true, as you also have experienced. That's because as heat is added there's also some heat lost to the environment. The higher the temperature difference between the adapter and the surrounding air, the more heat it will lose. So with rising temperature finally you will reach an equilibrium where the amount of dissipated energy equals the amount of lost energy, and then temperature won't rise anymore.  

So, this equilibrium depends on temperature difference. If your adapter will go to 50°C in a 20°C room, it will go to 60°C in a 30°C room. It needs the same difference to get rid of the same amount of energy.  

The designers of these adapters know that they will get hot, and have accounted for a certain environment temperature at maximum power. In normal conditions you should be safe, but the adapter will no doubt fail quickly when used in a 85°C sauna. That's the reason sauna's normally don't have electronics (I haven't seen any so far); they use the good old hourglass as timer.