Infinite heat from gas? Does any type of gas keep the same temperature if is constantly exposed to same force? In other words, must we change the applied force in some moment to get heat again, or is the same constant force enough to force gas to continue heating up?
I'm thinking about pistons. Imagine that you have a simple piston with gas inside and on that piston some constant force is applied (forever). Will the gas produce (because it is compressed) constant amount of heat (forever)?
 A: To increase the energy and temperature of the gas, you need a force and a displacement of the agent of the force, in this case the piston  ($\mathrm{d}E = - p\,\mathrm{d}V$)  A constant force with no displacement will not increase the energy and temperature of the gas.   Any force, constant or not, with a displacement will increase the energy.
The increase of the energy of the gas comes from collisions between the atoms at the surface of the piston with atoms in the gas.  If the piston is in motion, the collisions will transfer kinetic energy from the atoms of the piston to the atoms of the gas.  (You can see this if you study the elementary treatment of a one-dimensional elastic collision between two moving objects.)  If the piston is not in motion, gas atoms that collide with the piston bounce off with the same kinetic energy as they came in with: no increase of energy or temperature.
Update:
@Aksakai reminds me that my answer is incomplete, as I did not specify in detail the surroundings of the system, and whether or not energy can be transferred to whatever is outside the piston.
But to give a clear answer to the original quesiton, you do not need to change the force to increase the temperature of the gas.  A constant force can do the job.
A: you have an open system, i.e. the heat is removed from gas through its walls. when the gas cools down, it shrinks, so the piston will squeeze into the chamber. since you still apply the force, gas will heat up, and heat will be removed through walls again. while gas shrinks more it'll be more and more difficult to remove heat from walls, because of finite heat transfer of the walls. at some point the gas will shrink so slowly that you may say it simply stopped shrinking at all for all practical purposes.
