Why does the A8 have twice as many transistors than the Haswell processor yet runs on less power?
It is the clock frequency, i.e. frequency of the switching, and the number of transistors actually being switched at the same time that consume the power, and consequently, generate the heat, and not the number of transistors.

For example there could be a large amount of transistors in a area of the die that aren't being used, and so, if they are in the off (closed) state, then they will not draw any current, so less energy and less heat.

However, if some active area is switching at a higher clock frequency, then (on average) they are open for more of the time, and so draw more current, thus energy and heat.

Hope that helps.