Dependence of H on T
Keeping the pressure constant, the dependence of H on temperature is given by the expression: \begin{equation} \left(\frac{\partial H}{\partial T}\right)_P=C_P \end{equation}
Dependence of H with P
To calculate $\left(\frac{\partial H}{\partial P}\right)_T$ we use the Gibbs equation $dH=TdS+VdP$ keeping the temperature constant. \begin{equation} \left(\frac{\partial H}{\partial P}\right)_T=T\left(\frac{\partial S}{\partial P}\right)_T + V=-TV \alpha +V \end{equation} In the last step, Maxwell's equations were used.