Lattice QCD can be used to study the QCD phase diagram at finite temperature and zero density. Non-zero density is implemented on the lattice using the chemical potential however this gives a possibility of a complex probability which means the statistical machinery normally used breaks down. Switching the gauge group from three colour to two colour avoids this problem. Simulating two colour QCD allows for investigation into the thermodynamic phase transitions of a theory which is similar to three colour QCD. Confinement and asymptotic freedom are observed, however the definitions for hadrons differ. To study the thermodynamics we use the derivative method which requires the determination of the Karsch coefficients. Previous studies determined these coefficients perturbatively however this led to negative values for pressure. Non-perturbative studies have proved difficult due to the computational cost and accuracy required. We attempt to determine these coefficients non-perturbatively and review possible improvements in setup and calculation. We finish with thermodynamic results for the pressure, energy density and trace anomaly.