Fictional physics validity - Radio waves raising temperature?

[elementcollector1]

Spotted this playing one of my old Pokemon games under the Pokedex entry for Magneton:

"It is actually three Magnemite linked by magnetism. It generates powerful radio waves that raise temperatures by 3.6 degrees F within a 3,300-foot radius."

That got me wondering how much power that would actually need, and whether it would be feasible for Magneton to actually output it via microwave radiation. Best equation I could find was the heat capacity equation (altered for power instead of energy):

P = mcΔT/t
(P = power in watts, m = mass in kg, c = heat capacity in J/kg.K, ΔT = temperature change in Kelvin, and t = time in seconds)

We know ΔT is 2 K,  and I'm assuming c is the value for water vapor (steam) at 1996 J/kg.K.

m is a bit trickier - I assumed an average relative humidity of 30%, which gives 0.0066 kg water vapor per cubic meter air. In non-Imperial games, that 3300 feet is replaced with 1000 meters, so I'll use a sphere of 1000 meter radius for Magneton's maximum influence, which has a volume of 4.1887902 x 10⁹ m³, giving a total water content of 27646015.3 kg.

t is also tricky - I assumed Magneton takes one hour (or 3600 seconds) to achieve this temperature rise. No real reason behind the assumption other than giving it plenty of time.

From all this, I get a value of 3.0656359.2 x 10⁷ W, which seems pretty realistic given the sheer mass of water being heated (and pretty terrifying for a lone Pokemon to be outputting somewhere in the wilderness). However, I want to take into account more complex factors, such as attenuation of the radiation, the frequency of the microwave (which I'm assuming is 2.45 GHz, since that's the one commonly used in commercial microwave ovens). I found this graph for attenuation of a range of EM frequencies from oxygen and water:

However, I'm not quite sure how to factor all this stuff in. Plus, assuming the number doesn't drop too much, what would be the temperature one meter from Magneton? What would be some other consequences of that much microwave radiation in the atmosphere?

 

[elementcollector1]

I ended up trying this again, this time using radiation physics for a different approach. This time, I assumed Magneton and its surroundings had reached thermal equilibrium, so time is no longer a factor (but is presumed to be quite a while).

I started by getting the solid angle of an area 1km from Magneton, assuming Magneton could be expressed as a 1.0m diameter sphere. This got me an angle of 3.1415 x 10^-6 steradians.

From here, I (maybe correctly?) asserted that because Magneton and its surroundings both started at the same ambient temperature, the temperature added by radiation could be estimated via the following equation (taken from here) and used to solve for Magneton's surface temperature (again added to the ambient temperature):

ΔT = +2 K = ((ΔT_Magneton)⁴ (3.1415 x 10^-6) / (4pi))^1/4

=> ΔT_Magneton = 89.45 K

I then went back and altered the solid angle's distance to get the temperatures at 750, 500, 250 and 1 m from Magneton using this same ΔT_Magneton, and graphed these to find the following equation:

ΔT = 63.251d^-1/2

Where d is the distance from Magneton in meters. Integrating this from d=1 to d=1000 to find the area and then dividing it by the distance of 999 m between the two points, I found the 'global' temperature increase within the 1 km sphere to be an average of 4.004 K, which seems pretty reasonable.

Lastly, we can add this temperature increase to the average global temperature (I picked 1998's value of 58 ^oF or 287.594 K because this was when the game came out) and use the Stefan-Boltzmann Law to calculate the energy density in Joules/cubic meter of the 1 km sphere Magneton is inside, followed by the total energy in Joules to maintain this temperature inside the 1 km sphere.

p_E = (287.594 + 4.004)⁴ (5.6625 x 10^-8) (4/(3 x 10⁸)) = 5.459 x 10^-6 J/m³

E = (5.459 x 10^-6 J/m³) (4/3)(pi)(1000³) = 22,866 J

This is a surprisingly small amount, which I think makes sense at thermal equilibrium, but why is it so much different than the one calculated previously?

Also, would I be right in saying 23 kJ/s or 23 kW is needed for Magneton to maintain this temperature increase every second? So not only is it hot enough to boil water on contact, Magneton is also pumping 23 kW of microwave radiation into its surroundings. Anything nearby is going to get cooked pretty quickly (temperature at 1 m under these assumptions was +63.25 K, meaning a nearby Trainer or Pokemon is in a lot of trouble unless they have RF shielding...)