Flaw in my logic on Henry's Law? It states mathematically $ p=Kx $ where $x$ is mole fraction of dissolved gas and $p$ is partial pressure of the gas.
Dissolution of gases is exothermic, so with increase in temperature, solubility $x$ decreases.
But increase in temperature also means an increase in partial pressure $p$ which in turn means an increase in solubility $x$. Where am I going wrong?
Henry's law is: 


  At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. 


If temperature changes, the Henry's law constant itself changes.