Temperature is known to have a lower limit, absolute zero corresponding to a temperature of 0K. Is there also an upper limit above which matter as we know it cannot exist? This paper is aimed at obtaining a theory for the establishment of a possible upper limit to temperature, with the use of concepts from thermodynamics and special relativity. This is done by using the kinetic theory and ideal gas equation to obtain an expression of temperature as a function of velocity of the particles, then using special relativity to establish the speed of light as a velocity barrier, thus providing a corresponding upper limit to temperature. Such a temperature should be unreachable, or the particles would be moving at the speed of light, which is against the second postulate of special relativity. This approach leads to results indicating the existence of not one but several temperature limits, characteristic to each element.