Gain peak shifts with injection in undoped and p-doped InAs quantum dot laser structures between 200 K and 350 K are measured. The blue-shift with increasing injection, due to state-filling of the inhomogeneous distribution, is temperature independent for a fixed peak gain in the undoped sample, but temperature dependent in the doped sample. This is due to the wide electron state distribution and lowering of the electron quasi Fermi level by p-doping relative to the undoped device. While p-doping reduces the temperature dependence of the threshold current, it comes at the expense of increasing the temperature sensitivity of the wavelength.