They can't move to the cool side if the difference isn't noticeable. Many misunderstand how hot these bulbs really are because it is difficult to get a measurement of the effect with a thermometer.
But, 250w lamps are meant for a 6' cardboard circle in a barn. That was what they were designed for. If you have a smaller space, you are risking cooking the chicks.
Heat plates are easier, safer, and use less energy. Plus, the chicks get to have a natural day/night cycle.