According to the theory of special relativity in physics, the speed of light in a vacuum (denoted as "c") is an absolute speed limit in the universe. It is considered the maximum speed that any particle or information can travel.
As the temperature of a system increases, the average kinetic energy of its constituent particles (such as atoms and molecules) also increases. This leads to an increase in the speed of individual particles. However, the relationship between temperature and particle speed is not linear. At higher temperatures, the speed distribution of particles follows a statistical distribution known as the Maxwell-Boltzmann distribution.
While it is true that increasing the temperature of a system can result in faster-moving particles, this does not imply that their speeds can exceed the speed of light. Special relativity dictates that as an object with mass approaches the speed of light, its energy and momentum increase dramatically, making it increasingly difficult to accelerate further. It would require an infinite amount of energy to accelerate a massive object to reach or surpass the speed of light.
Furthermore, the concept of temperature becomes less well-defined and conventional thermodynamic laws break down when dealing with extremely high temperatures or energies close to the Planck scale (the scale at which quantum effects become significant). In these extreme regimes, our current understanding of physics, including the theory of special relativity, is insufficient, and a complete theory of quantum gravity is needed.
In summary, according to our current understanding of physics, it is not possible to continuously heat a system to such an extent that the speeds of its constituent particles exceed the speed of light. The speed of light remains an absolute cosmic speed limit.