The temperature is proportional to the energy of the system only for ideal monoatomic gases. (Ideal diatomic gases, are slightly more complicated.)
So a "hot" Helium balloon where all the particles are moving in random directions has a different temperature than a "fast" Helium balloon where all the particles are moving roughly in the same direction. It doesn't matter how difficult is to define it. (Probably you can use an infrared thermometer pointed in the direction perpendicular to the movement to get the correct temperature.)
In the fast balloon you can theoretically split the energy in A: kinetic energy of the center of mass and B: internal thermal energy, so the total energy is A+B. With some device you can extract all the kinetic energy as something useful. (for example, make the balloon hit some lever connected to an electric generator, you will need something more smarter to get the 100% of A but it's theoretically possible.) So you can extract the 100% of A
If the hot balloon with the same energy you have only A+B of internal thermal energy. If you use some device you can never extract the energy, you can never extract more than a part of B as something useful like electricity, because of the second law of thermodynamics. It the ambient temperature is T_amb and the initial temperature of the balloon is T_bal, you can get at most B * (1 - T_amb / T_bal) as something usefull like electricity and waste at least B * (T_amb / T_bal) in a heat sink.
So, to get back to the original point, your position is that a single particle in isolation can't have a temperature because its entropy (or rather the change thereof) is 0, so the equation breaks.
I suppose it comes down to whether you define temperature as "what thermometers measure" or the average potentially transmissible energy of an ensemble. I prefer the latter definition for its clarity, but like the idea of kolmogorov complexity, it is sometimes unwieldy in practice.