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According to established theories, there is no maximum.
No maximum to density... No maximum for density because of singularities... Don't ask me about singularities because it is a belief which you know i disbelieve... 
But temperature isn't about absolute motion. The temperature of a single particle is meaningless. It's only when you have a system of particles that you can talk about the system's temperature. If the velocity of the particles relative to each other is low, you have a low temperature system. It doesn't matter how fast that system is moving relative to you.
So we have created a system where, as we add more and more energy, temperature starts off positive, approaches positive infinity as maximum entropy is approached, with half of all spins up. After that, the temperature becomes negative infinite, coming down in magnitude toward zero, but always negative, as the energy increases toward maximum. When the system has negative temperature, it is hotter than when it is has positive temperature. If you take two copies of the system, one with positive and one with negative temperature, and put them in thermal contact, heat will flow from the negative-temperature system into the positive-temperature system.