Where does the extra energy go when walking vs biking? We burn a lot more Calories when walking a mile vs biking a mile. Why? Where does the extra energy burned from walking go? Is it that the mechanics cause the body to generate a lot more heat energy when walking than when biking, and that energy is wasted to the environment when it could be used as kinetic energy to propel the body forward?
 A: 
We burn a lot more Calories when walking a mile vs biking a mile.

The accepted answer in the link provided in one of the other answers shows that inertia is the key why less calories are burned biking than walking. As it states "When you're riding a bike on a level gradient you just need to give it a push to get going, then you can coast for quite a while before friction and air resistance slow you down. In other words, the relatively frictionless wheels mean the bicycle's kinetic energy doesn't dissipate quickly". In contrast, when you walk, you need to exert a backwards force on the ground over the entire distance.
But the more general concept is that physical effort does not always equal physics work.  In the extreme case, if you stand holding a very heavy object in place without lifting it, you do no physics work yet the effort required to hold the object burns more calories than if you weren't holding it. Richard Feynman explains it this way in his physics lectures:
The fact that we have to generate effort to hold up a weight is simply due to to the design of striated muscle. What happens is when a nerve impulse reaches a muscle fiber, the fiber gives a little twitch and then relaxes, so that when we hold something up , enormous volleys of nerve impulses are coming in to the muscle, large numbers of twitches are maintaining the weight, while other fibers relax. When we hold a heavy weight we get tired, begin to shake, ...because the muscle is tired and not reacting fast enough.
Essentially, the extra calories burned due to muscle activity increases the bodies internal energy. That would raise its temperature if it were not for the body's ability to regulate its temperature via perspiration, more rapid respiration, etc.
Hope this helps.
A: The extra energy ends up as heat radiated by your body. At first the energy is internal thermal energy of your muscles. This is then moved out of your body by your circulatory system. The higher-temperature muscles heat the blood passing thorough them. The circulatory system moves the energy around and increases blood flow to the skin where the heated blood can radiate to the environment and contribute to the evaporation of sweat. The cause of the increased thermal internal energy of your muscles is caused by inefficiency of the biological process that converts chemical potential energy to mechanical work.
For reasons why walking requires more mechanical work per unit distance than bicycling on level ground, see this question about running vs bicycling.
