What happens to the partial pressure of carbon dioxide in a sample of air if the temperature of the air sample is increased

The proportion of pressure exerted by carbon dioxide will remain constant in the sample. However, from Gay-Lussac's law that P1/T1 = P2/T2, if the temperature rises, the total pressure of a gas (either pure or mixture) increases. Therefore, the partial pressure increases, even though the proportion relative to the total air sample stays the same.