A weather station records the noon temperature on many days of a month…

Step 1. Fahrenheit. The mean is $1.8 \times 20 + 32 = 68\ ^\circ\text{F}$. The standard deviation is $1.8 \times 3 = 5.4\ ^\circ\text{F}$. The shift $32$ does not enter the spread.

Step 2. Kelvin. The mean is $20 + 273.15 = 293.15\ \text{K}$. The standard deviation stays $3\ \text{K}$, because a kelvin and a degree Celsius are the same size.

Step 3. The three coefficients. In Celsius, $\dfrac{3}{20} \times 100 = 15\%$. In Fahrenheit, $\dfrac{5.4}{68} \times 100 = 7.94\%$. In kelvin, $\dfrac{3}{293.15} \times 100 = 1.02\%$.

What it means. The same weather gives three different coefficients, because each scale puts its zero in a different place. A temperature on these scales has no true zero for "no heat" except kelvin, and even there the figure only tells the size of the spread against absolute temperature. So the coefficient of variation is not used for Celsius or Fahrenheit data.