Will this type of engine produce thrust? I was wondering that if we replace the combustion chambers in a jet engine with heaters heating the compressed air up to temperature near to plasma then what will be the case, will it produce any kind of thrust or it will be just useless
 A: This is the main idea behind laser-driven heat exchanger propulsion:

The laser beam heats a solid heat exchanger, which in turn heats an
  inert liquid propellant, converting it to hot gas which is exhausted
  through a conventional nozzle. This is similar in principle to nuclear
  thermal and solar thermal propulsion. Using a large flat heat
  exchanger allows the laser beam to shine directly on the heat
  exchanger without focusing optics on the vehicle. The HX thruster has
  the advantage of working equally well with any laser wavelength and
  both CW and pulsed lasers, and of having an efficiency approaching
  100%. The HX thruster is limited by the heat exchanger material and by
  radiative losses to relatively low gas temperatures, typically 1000 -
  2000 C, but with hydrogen propellant, that provides sufficient
  specific impulse (600 – 800 seconds) to allow single stage vehicles to
  reach low Earth orbit.

The lightcraft is another variation, but that doesn't rely on any fuel, it simply uses the shape of side mirrors to focus the laser into the surrounding air and provide thrust

A: The problem here (as Michael mentioned) is, there's no relation between heat and thrust. In fact, compressing the mixture produces heat, which helps to ignite the fuel along with compressed air. The gases, occupying more volume is exhausted out through the nozzle which helps thrusting the aircraft.
Your engine doesn't produce any thrust at all. In your case, there's a pumping propeller. You're just heating the air flowing through the heater. At higher velocities, the effect is negligible. I can't think of higher velocities because the aircraft can get no thrust using an engine, where air flows in and out..!
You may argue that hot air expands. But, simply heating the air in an airflow won't push the heater to the front (it's very negligible to be noticed). As I've mentioned earlier, more volume is exhausted in an engine since liquid has changed into a gas mixture. Here, the same air comes out (i.e.) $V_{in}=V_{out}$ which doesn't do much good for an aircraft.

Response based on Revision: Again, the thrust doesn't depend on how much you heat the stuff inside. It does, but it's based on how much kinetic energy, the gas volume (sucked inside) obtains, so that the contribution by the outgoing gas lump (as a whole) corresponds to your thrust. Returning to your question, I think it's quite ambiguous.


*

*Firstly, as far as I know, no known chamber exists. Recall the phrase. The fuel sprinkled on the compressed "air lump" isn't just good enough to heat it to plasma.

*Even if you've managed to heat the thing somehow to attain plasma, I can bet bet you that the chamber will be able to hold it, as time goes on. As far as I can say, the material gets fried up..!!!

*There are other issues in holding plasma, as it's a giant bulk of ions. I don't wanna go into it, as I've come to the conclusion that such a thing is just fiction. The engine's gonna cease out for sure ;-)

A: The main difference between what you have and a jet engine is the incoming cold air needs to be compressed, so the heater expands pressurized air which thrusts out the back.
The thrust is because the momentum flux out the back (i.e. mass times velocity per second) is larger than the momentum flux in the front.
The mass per second is the same, front and back, but the velocity is higher at the back because it has been heated to a larger volume.
What keeps it from blowing out the front is the fact that the pressure is high coming out of the compressor.
Usually what drives the compressor is a small turbine that takes away a portion of the energy in the exhaust stream.
Anything that compresses the air in front will do the job. A ramjet does it by simply using the ram pressure of air from the moving vehicle.
