[jeffreyH (OP)]

What would be the temperature of a gamma ray compared to a radio wave.

[alancalverd]

Temperature is the mean kinetic energy of a large number of particles, so strictly speaking a single photon cannot have a temperature. However the energy of a gamma ray can be anything from a few eV to more than 10²⁰ eV. Radio waves have energy < 0.001 eV.

[evan_au]

We can more easily turn the question around, and say: For a given temperature, what is the probability that it will emit a photon of a given wavelength?

In principle, an object at a given temperature could emit a photon of any wavelength - it's just that some wavelengths are far more likely than others. The distribution of wavelengths for "Black Body Radiation" is given by Plank's Law, see: https://en.wikipedia.org/wiki/Planck%27s_law

For an object the same temperature as the surface of the Sun (about 5500K), the most likely wavelengths are in the visible range, with less in the Ultraviolet range, and less in the infra-red (but there is still a lot in the very broad range we call infra-red).

If we measure the temperature T in degrees Kelvin (ie degrees above absolute zero), only 0.01% of the radiation from a "black body" is at a wavelength shorter than 910/T µm.

If we see on object emit a visible photon, it is highly unlikely that it has a temperature below 500K.

Similarly, if we see an object emit a gamma ray or X-Ray photon, it is extremely unlikely to come from something the temperature of the Sun's surface. (We can take pictures of the Sun in X-Rays, but that is because the Sun's corona is hundreds of times hotter than the Sun's surface.)

In practice, gamma rays tend to come from nuclear events, rather than the lower-energy interactions of electrons and protons which produce photons up to X-Ray frequencies (but there is some overlap, in that gamma ray photons from Technetium 99m can also be generated by X-Ray machines).

Edit: Clarified that I was talking about "Black Body Radiation". Thanks, Hamdani.

[hamdani yusuf]

If we measure the temperature T in degrees Kelvin (ie degrees above absolute zero), only 0.01% of the radiation from a "black body" is at a wavelength shorter than 910/T µm.

When stated the temperature in Kelvin, we should omit the degree.

[hamdani yusuf]

If we see on object emit a visible photon, it is highly unlikely that it has a temperature below 500K.

That is true for thermal radiation. But low temperature objects can also emit visible light, such as fireflies, LED, fluorescent lamps.