Hint: Your calculations will need to include calculating the fourth root of some number. (money.stackexchange.com)
In theory, any warming should be proportional to the fourth root of (wattage new / wattage old) and the wattage change should be proportional to the logaritm of the change in CO2 - that would give small temperature changes quite difficult to measure through the background noise. (wattsupwiththat.com)