I think your reasoning is sound.
However, being in Melbourne, Australia (which is heading for 35 C today), I can think of better applications of eating ice than burning calories. You would certainly experience a greater drop in body temperature by consuming equal amounts of ice versus water at 0 C.
Conservation of energy says that the sum of all energy in and out of a system must be equal to the change of internal energy of that system. So if you say that the system (say, your TV) remains in the same state (it doesn't get warmer over time), then the power in must equal the power out.
Now for an electrical device that gets all its power in through the electrical supply, there are broadly three different ways for power to come out.
- Heat
- Electromagnetic radiation (light, radio waves, etc)
- Work (rotation of a drill, motion of air from loudspeaker, elevator car being lifted, ...)
Very often, "heat" is an unwanted side effect of the conversion of electrical power into "something useful" - for example, an incandescent light bulb converts a lot of the power into heat, and only a little bit into visible light.
It is entirely possible that different devices will have different efficiencies, and will therefore produce a different amount of heat - it all depends what fraction of the electrical energy coming in is being converted to the other types of output.
For the case of the plasma TV, the mechanism for generating light is somewhat inefficient - see for example http://electronics.howstuffworks.com/plasma-display2.htm . Ionizing the gas so it can emit light requires quite a lot of power - so although the plasma TV excels in its range of intensities, color, and response time, all this comes at the expense of power consumption. By contrast, a LCD based screen uses a relatively efficient source of lighting (for example, LED or fluorescent lighting) and then uses the LCD to stop some or all of that light from reaching the viewer. So a LCD screen is "always on" - that is, always generating light - but for a dark scene it will re-absorb most of the light generated. A plasma screen will actually use less energy for a dark scene - it is simply not generating as much light to begin with.
Best Answer
tl;dr: Yes. Specific heat and temperature are different measurements.
The specific heat of a material is a function of temperature that describes how much heat it takes to change the temperature of a material by a specific amount $\frac{dU}{dT}$. Statistical mechanics concerns itself with questions like this. If we integrate the specific heat function from $0K$ to the temperature in question, we find a measure of an object's 'heat energy'.
Temperature, on the other hand, describes the tendency for an object to give up energy. In differential form, $\frac{dU}{dS}$, it's the change in internal energy with respect to entropy. A warmer object with less heat (tungsten, for example) may absolutely be more likely to give up heat than colder object with more heat (water, for example).
As far as the heat pump explanations, I'd encourage you to pull the refrigerator off the wall and touch the radiation coils on the back - they are in fact warm.