Seriously, it doesn't.
Allow me to present this image:
As mixture leans out above stoichiometric efficiency increases. Higher efficiency means higher heat (more or less by definition, if you're getting more energy out, you're getting more heat). Once you get past the trough of the curve it cools down again as you're then past maximum efficiency.
Stoichiometric just means there is exactly enough oxygen for the fuel. Running slightly leaner means that the fuel will tend to burn slightly faster; combustion relies on fuel and oxygen molecules colliding in the vapour phase and reacting, more oxygen means more chance for a fuel molecule to collide with one. However you also need proximity between reactions; too much air (i.e. very lean) leaves too much space between reactions which then slows the reaction down. This is also why EGR is so effective, you're adding excess nitrogen to the mixture which slows combustion reducing temperatures.
This gives the graph above, as you go past stoichiometric the increased oxygen increases reaction rate and give better efficiency (and heat) until the reduction in reaction rate from too much air overtakes it and reduces the efficiency.
Yes. Petrol cars run very close to stoichiometric most of the time (closed loop mode) because running rich or lean for too long will damage the catalytic converter or give poor emissions (or both). When you floor it the ECU will go into open loop mode where it just chucks in fuel to keep temperatures down, but this is inefficient. 30+ years ago badass would have been correct as carburetted petrols did tend to run slightly rich all the time.
The typical regime is actually to run very slightly rich and very slightly lean in an oscillation (typically 0.01 lambda difference or there abouts, so really very slight). This gives better cat performance than running bang on lambda = 1 all the time.