Is there an opposite to absolute zero?

Just thinking out loud...yes there should be. Temperature is basically just the vibrations of particles. If you increase the temperature enough you should get to a point where the particle is basically vibrating near the speed of light. At this point the particle may cease to be and become fundamental particles, i.e. quarks, but like the original particle they have finite mass and therefore cannot exceed the speed of light, so therefore must have a limited speed. As more energy is given to the particles the mass would increase instead, therefore raising the temperature, but there must come a point where the mass of the particle compared to its size becomes a miniature 'black hole' to which the energy now given just goes to increase the particles gravitational field and the temperature drops to near enough absolute zero (as black holes have been calculated to have temperatures around that level). Now assuming this is correct, there should be a peak an instant before the particle crosses the black hole boundary to which is the maximum temperature of the particle. (Assumption made is that an infinite energy source is available, only acting with a small finite number of particles and they are in a container infinitely bigger than the particle itself)

There is in fact a possible maximum temperature. This temperature would be the temperature of a black body that emits an energy density equal to that of matter. By setting the value of the Stefan-Boltzmann equation for black body radiation equal to the energy density of matter (e=mc2) one can calculate a black body temperature that would radiate an energy density equal to that of matter, if matter is indeed the densest form of energy. I performed this calculation about 25 years ago as a graduate student and found this temperature to be on the order of 10^23 K. The proposition here is that a black body cannot emit an energy density greater than that of matter.

The answer to this question as stated is "No." Any unbounded physical system will discorporate at some high temperature at which its component particles are no longer bound to one another. The temperature of a system of noninteracting particles is a meaningless concept, so we must constrain the system in some way.

The question may be recast. Let us ask instead if there is some upper bound to the temperature of a system which is confined to a rigidly bounded volume V. I believe the answer to this question is also "No." Since for any given equilibrium state of our hypothetical system there exists a higher temperature equilibrium state having one more photon (on average), there is no upper bound to the temperature of a system thus constrained.

In relativity, kinetic energy is NOT proportional to v squared, so it can grow without limits even if v must be lower than c.

Is there a maximum temperature for a gas or plasma? I guess that's the main question, for we're certainly talking about temperatures above the boiling point or ionization limit of any matter. Then, I guess the answer comes down to - is there a maximum to the kinetic energy the particles can have. That would suggest the Planck temperature for point particles. But assume a gas of black holes, each with a mass of a few suns, say 2 10^32 kg, and a relative velocity of only 100 km/s (comparable to the orbital velocity of Earth). The average kinetic energy per particle is 10^42 J, corresponding to a Maxwell-Boltzmann temperature of about 5 10^64 K , quite a bit hotter than the Planck temperature. And I don't think this -literally- astronomical temperature is unrealistic in any sense. This isn't the limit, if we assume super-massive black holes and relatvistic velocities, we could go up maybe ten orders of magnitude.

Interestingly, the radiation (Hawking) temperature of each of the black holes would be among the lowest temperatures in existence.

Other argumentation can lead to nearby conclusion: From the definition of absolute temperature T for a system, 1/T = dS/dU, where S is the entropy and U the internal energy,
If we are dealing with a very large finite system, following the approach to compute entropy as: S= k.ln(W), where W is the "thermodynamic probability", for a finite system (with upper bound in energy, if energy is not bounded one could "create" more particles) it goes as a (very large) set of discrete points (S-U), of which there is a maximum in S versus U, which would eventually give the "infinite temperature point". But, temperature is a statistical concept, you should not expect an "exact" value without implying an infinite time. Moreover, we measure always with incertitudes (or at least, with quantum limits: to assure the system has exactly the "correct" energy, we would need infinite time). So, we should not expect (in a finite time) to find an "infinite temperature" in any system (even if experiments have been conducted on magnetic systems at "negative absolute temperatures", which would be beyond the "infinite temperature")
Further on, if one has to "wait infinite time" to see "infinite temperature", the same kind of quantum argument about the determination of energy would lead to the need to "wait infinite time" to see an "absolute zero temperature" in a finite system... and we are only measuring over finite times...

As a layman I found Greg Lawton's theory to be the most convincing and elegant using the familiar E=MC2 equation.