The Temperature of the Universe After the Big Bang

Question: When I think about the first second after the Big Bang, my understanding is that as we look backward toward t equals zero, the temperature becomes hotter and hotter until we approach infinite temperature. But when I think about what temperature is, I know it has to do with motion. Carlo Raveli tells us the time is the order of events. From that perspective, I wonder if we can say that the temperature becomes time-like as it reaches infinity,. such that the first second might as well have been an eternity.