Is temperature a discrete or continuous variable?

Temperature is a continuous variable.

Temperature is a continuous variable because its value can assume any value from the set of real numbers between -273 degrees Celsius (absolute zero) to positive infinity.

Discrete variables are those variables which value can be whole number only while continuous variables are those whose value can be both whole numbers and fractional number. For example: population of a country is discrete variable as it cannot be with fractional values.

Temperature is continuous variable as it does have fractional value too. For example: Today's temperature is 30.5 degree Celsius, here 30.5 is not a discrete variable and hence is a continuous variable. It has wide range and its value is true for all real numbers.