You too are obviously well versed in wave physics - my background is Biotechnology w/ specialization in biophysics.
I was really hoping to avoid the E + M wave aspect actually.
Looking at the vector cross-product function above, I assume that H is the magnetic portion of the wavefront?
None the less, the "power" can still be calculated through basic wave-equations (similar to simple harmonic motion). As you correctly noted, the RMS values are used as opposed to absolute.
As you stated, the frequencies involved are non-ionizing and thus are unable to cause bond dissociation (hence the non-polarizing).
The trouble with the heating argument is that the human body is highly adapted to thermoregulation. As you are surely aware, the average specific heat capacity for the human body (similar to water) is 3470 J/kg'C. In short, we are great heat-sinks. Furthermore, the thermal conductivity of human tissue (excluding blood) is 0.2 J/s'Cm (Joules per second degree metre) and blood has a thermal conductivity of approx 0.4 J/s'Cm.
What does all this mean?
As a body part is heated, the heat is moved fairly efficiently through out the entire system - then into the surroundings. All the data I have seen regarding near-range radio transmissions have produced such little energy that even assuming 100% thermal adsorption, the heat would be conducted and transported away at a rate exceeding the rate of input.
As I am sure you are aware, the thermal adsorption would be
well below 100% and so very little energy is transfered.
Again the question though: how would the tissue be heated?
As a point of interest, I will look into the resonant frequency of cytosol (in a simplistic sense, the "goo" that is the cytoplasm of a cell).
I asked a close friend of mine (physicist) about resonance of particles based on quarter, half, etc-wave frequencies. The principle of maximum heat-transfer is dependant on distance between antenna and medium. As an example, microwave ovens have a wavelength of 10cm and thus, maximum heating ocurrs at 10cm, and other "efficient spots" would be 5cm and 2.5cm. It seems that the frequency plays a major role on the areas of tissue which would receive "maximum heating". Interesting.
All said, we would have to start looking into the thermodynamics of the system (tissue) and the surroundings (body) to better understand the issue.
Coming back to the 45Mhz transmitter question: these devices are such poor transmitters (low power) that I would expect you could heat a glass of water from 20'C to 21'C in about 10 years (assuming no loss of heat to the surroundings). I wouldn't worry.