There are actually two separate questions here. First, how fast do the skateboards lose energy and, second, how fast do the wheels, bearings, etc., change temperature? The rate of energy loss of the skateboards -- how fast they stop -- is determined by the frictional force between the bearings and the wheels and perhaps the ground if the skateboards aren't rolling perfectly (I am assuming that you're pushing the skateboards with the same speed to start with). The more friction, the faster the skateboard will stop. As you've noted, the energy lost from the skateboard goes into the wheels, bearings, etc., and is converted to heat energy. What the heat capacity does is determine the change in temperature of the wheels, etc., given a certain amount of heat energy -- which used to be the kinetic energy of the skateboards. So, even though the skateboards might lose the same amount of kinetic energy in the same time, the wheels and ball bearings of one would get hotter than the other. But the skateboards would stop at the same time as long as the friction is the same!

Try to come up with an experiment to test this!

No, the heat capacity is just a measure of how much the temperature of the bearings, etc. will change for a given amount of heat. So, if the friction coefficients are the same, they will roll the same distance, but A will be a higher temperature at the end. Now, if the temperature difference is enough to boil off the bearing grease, then that changes things.

Most of the heat is in the ground, although on a practical surface, there is substantial energy loss in the form of media grinding -- i.e. sand being subdivided and mixed into the viscous pavement. (This mostly ends up in the substrate as heat). Another substantial loss is sound generation. The ball bearings have relatively lower loss -- roll the skate board on a smooth surface vs. a rough one, measure the distance -- then try with different bearings, i.e. sleve... Sleve bearings won't last long, but will prove the point. If the bearings had much lower heat capacity, then by definition, the frictional heat would cause a much larger change in operation temperature. This would impare their function and increase the friction substantially. However, it is often the case that the operating temperature range is more important than the heat capacity. For example, car brake disks and drums are invariably made from cast iron despite aluminum's much greater heat capacity -- aluminum weakens at much lower temperatures than cast iron, and at high temperatures, the heat loss from convection in the atmosphere is the primary means of cooling. (Steel is not used because it has a tendency to "creep" at such temperatures, which is largely eliminated by the large crystals in cast iron.) Upshot, if the skate board is run fast enough to heat the bearings substantially, it is more important to make sure that they operate at that temperature than that they could store the heat internally as added heat capacity. This would not be true if heat superconductors existed at these temperatures...

This is a great question because it is difficult to answer and raises several important issues. It's not obvious to me, and it would be difficult to measure, whether more energy is lost as heat in the wheels, ground, or bearings. The primary agent that dissipates energy is friction. Rub your hand on something smooth like a desktop and something less smooth like a denim pant-leg. The rougher the rubbing, the more heat is generated. With this in mind, the answer to your second question is No. Heat capacity is NOT a measure of how much energy a material will absorb. Given an amount of added energy, heat capacity is a measure of how hot a material will get. Thus, if skateboard B has a higher heat capacity, it would not necessarily absorb more or less energy than skateboard A, but it would become less hot. A skateboard rolling on a bumpier surface with older (less smooth) bearings will not roll as long because there is more friction. Whether more energy is lost in the bearings or the ground probably varies with the particular circumstances of the experiment.

There are other outlets for energy as well: The friction of air and the skateboard, and the displacement of air by the skateboard. Also, any deformation (bending or denting) of the wheels, the ground, or the bearings is a loss of kinetic energy. I can imagine several different classroom skateboard experiments with different wheels on different surfaces carrying different loads.