Re: Hair dryer in a can?

Heat can be thought of as "thermal energy".  For example, if you have a 
cool gas (room temperature air) and a hot item (heated pan), the air will 
pick up some of the energy from the pan and the pan will lose some energy 
to the air.  This occurs until thermal equilibrium sets in, when the 
temperatures are the same.  Because a pan is small, relative to the amount 
of air in the room (and the air's ability to absorb energy), the room 
doesn't get appreciably hotter.  This isn't the case when you use an oven, 
however, where your heated item is large and generates lots of heat.

Now, let's imagine this room temperature gas under pressure.  You've 
already noted that things seem to cool down when gas under pressure is 
released.  This is true.  It can be shown that:
 
      (T2/T1)= (P2/P1)^ (gamma)

Where T is temperature in kelvin, P is pressure (any units), gamma is the 
ratio Cp/Cv (= 5/3 for monoatomic gases and 7/5 for diatomic gases)
(reference:  Methods of Experimental Physics, Vol II Atoms and Molecules, 
F.B. Dunning and R. Hulet Eds.)

Then, as the pressure drops, the temperature of a gas drops as well 
(because of a requirement for conservation of entropy).  To generate heat, 
you'd have to reverse the process, adding energy.

To generate heat, you could use a chemical process (disposable hand 
warmers like you find at the outdoor recreation stores or a combustion 
reaction:  both liberate energy stroed as chemical bonds), or a physical 
process such as friction (bend a piece of plastic back and forth for a 
while and it will heat up).  An electrical process is a physical method, 
as electrons dissipate power through a friction-like mechanism in a 
resistor.

Hope this gets you started...
My advice to you would be to start with a process you understand very 
well, and apply it to a problem or question.  This is how many inventors 
find success.  For example, you noticed that air is cooled upon 
expansion.  Maybe think of a way to use that process, rather than try to 
make something happen which doesn't naturally.

Good luck,
Mike