would heating a stove to 400 degrees be more or less energy efficient if done more quickly? Would heating a stove to say 400 degrees be more or less energy efficient if done over a shorter or longer period of time? say 5 vs 10 minutes. Which would cost more on the electricity bill?
 A: Definitely faster is more efficient, because less of the heat energy would be lost by the heat transfer through the insulation (plus convection and radiation) over a shorter time.
While this question is mostly hypothetical, it has an important practical application. Consider you are in a warm kitchen cooking in winter and accidentally burn something that fills the kitchen with a smoke. Now you need to open a window to let the smoke out. The choice you face is to open a window only ajar to allow the smoke to escape little by little without cooling down the room or else open the window wide and let the smoke out instantly at the expense of filling the entire room with a freezing cold air. Which choice is more energy efficient?
Intuitively, the former, but no, the latter is the correct choice. The heat capacity of air is very small. Quickly replacing the entire volume of air in the room with a cold fresh air is not a big loss of energy. You'd be surprized how fast the fresh air would fully warm up, literally a minute or so. The heat capacity of the walls, furniture, and other objects in the room is orders of magnitude higher than the heat capacity of the air. A larger loss of energy would occur when a cold air cools down the walls over a longer period of time with the window open only ajar.
A good question, time is indeed a critical factor considering the heat efficiency in different situaltions, because it takes time for the heat energy to dissipate. 
