Depending on what you mean by “discontinuously” it always does: the microscopic world is “discrete”. Instead of thinking of “temperature” you may think of “inv

Depending on what you mean by “discontinuously” it always does: the microscopic world is “discrete”. Instead of thinking of “temperature” you may think of “inverse of temperature” and then there is no issue with that number going “continously” from very negative to very positive.