Re: Why does increasing temperature increase energy of molecules?

   It is probably easier to take this question the other way around.  When
the total amount of random kinetic energy shared by a group of molecules
increases then the thing we call temperature increases because it turns out
that the amount of random kinetic energy is what a thermometer measures.
    The molecules that make up any object are always moving about.  They
can rotate,  vibrate, or just travel in straight lines, some books will say
“translate”, until they bounce off another molecule.  Any of these motions
has some energy associated with it.  Thus the more quickly it spins the
more rotational energy it has, the greater its rate of vibration the more
vibrational energy it has and the more rapidly it travels between
collisions the greater its translational, or kinetic, energy.
   This motion is quite random so at any given time not all the molecules
will have the same kinetic energy and over time any given molecule will
continually gain and lose kinetic energy as it collides with its neighbors.
 The result is some distribution of kinetic energies among the molecules in
the sense that at any instant in time there will be a few with very little,
a few with a lot, and most with some amount in between. The most likely
shape of this distribution of kinetic energies is called the
Maxwell-Boltzmann distribution and there should be a figure in your
Chemistry text showing it.  It shows that the greater the total amount of
random kinetic energy shared between the molecules as they collide the
greater the number that will have a lot of energy.  The exact shape of the
curve is determined by the Temperature. 
    When you place a thermometer in contact with a material the molecules
in the material collide with the molecules of the thermometer and cause
them to come to the same average random kinetic energy as the material.  
All of this jostling around will cause the liquid column in the thermometer
to expand if the amount of jostling increases and vice versa.
    As far as reaction rates are concerned if the molecules move faster
then they hit harder.  They may also hit more often but what is usually
most important is that the faster they are moving when they collide the
more likely they are  to have enough collision energy to make and/or break
bonds to form new molecules with a different structure.
    Chemistry is a pretty violent process for the most part from a
molecules point of view.  As a chemist I find it very useful to try and
imagine how the world around me would look of I were a molecule and this
random shuffling about of different energies is a big part of that picture.
 Good luck with your chemistry and I hope you find the molecular world as
fascinating as I have.