No, the speed of atoms cannot exceed the speed of light, regardless of how high the temperature is or how much they are heated. According to the theory of relativity, which is a fundamental principle in physics, the speed of light in a vacuum is the maximum attainable speed in the universe. Nothing with mass can travel faster than the speed of light.
As the temperature of a system increases, the average kinetic energy of its constituent particles, such as atoms or molecules, also increases. This leads to an increase in the speed of the particles. However, as the particles approach the speed of light, their mass increases according to the theory of relativity. As a result, it requires more and more energy to accelerate them further.
When the speed of a massive object approaches the speed of light, its relativistic mass increases to the point where an infinite amount of energy would be needed to accelerate it to reach or exceed the speed of light. This is known as the mass-energy equivalence principle, expressed by Einstein's famous equation E=mc². So, no matter how high the temperature or how much energy is applied, it is impossible for particles with mass, such as atoms, to reach or surpass the speed of light.
Therefore, the notion of constantly heating a system to achieve speeds greater than the speed of light is not supported by our current understanding of physics. The theory of relativity provides a fundamental limit to the speed of particles with mass, including atoms.