Why is there no absolute maximum temperature?
I think the problem here is that you're being vague about the limits Special Relativity impose. Let's get this clarified by being a bit more precise.
The velocity of any particle is of course limited by the speed of light c. However, the theory of Special Relativity does not imply any limit on energy. In fact, as energy of a massive particle tends towards infinity, its velocity tends toward the speed of light. Specifically,
$$E = \text{rest mass energy} + \text{kinetic energy} = \gamma mc^2$$
where $\gamma = 1/\sqrt{1-(u/c)^2}$. Clearly, for any energy and thus any gamma, $u$ is still bounded from above by $c$.
We know that microscopic (internal) energy relates to macroscopic temperature by a constant factor (on the order of the Boltzmann constant), hence temperature of particles, like energy, has no real limit.
There is an absolute maximum temperature, and it is $0^{-}$. :)
Okay, that sounds silly, but look it up in L&L: Statistical Physics I.
Think about an Ising paramagnet in an external field: At "zero" temperature (or actually $0^{+}$) the free energy of a system will be minimized by a unique minimum energy configuration. As we raise the temperature, the number of microstates with slightly higher energy grows rapidly, so we have a lower free energy in these entropically favorable configurations. Now we continue all the way to infinite temperature, at which point the system becomes completely disordered.
But wait, what if we drive the system to even higher energy? In that case there are fewer microstates and so the derivative that defines temperature goes negative, and the temperature that corresponds to these configurations is $-\infty$. This actually corresponds to the principle of "population inversion" in lasers. Anyway, higher and higher energy configurations (with their continually decreasing entropy) correspond to decreasing negative temperatures, until all of the spins point against the external field at $T=0^-$.
The speed of light is an upper limit for the speed of a massive object, but there is no upper bound on the kinetic energy of an object. In fact, that's why the speed of light is an upper limit (one of many reasons, anyway)-- an object moving at the speed of light would have infinite kinetic energy.
The temperature is a measure of the average kinetic energy of particles in a sample. Since kinetic energy does not have an upper limit, temperature does not have an absolute maximum.
(In equations, the kinetic energy is: $K=(\gamma - 1)mc^2 = (\frac{1}{\sqrt{1-v^2/c^2}}-1)mc^2$ which becomes infinitely large as v gets very close to the speed of light c.)