An analysis of the transverse and longitudinal mode structure of broad area quantum dot lasers emitting at 1060nm is presented. In particular, temperature is shown to play an important role in the stabilisation of the transverse mode structure of the devices. In addition, the investigation of the the interaction between these transverse modes, through the measurement of the spatial intensity correlation, shows that the laser retains some modal properties in the unstable regime. Finally, measurements of spectral correlations between longitudinal mode groups display a strong dependency on their respective transverse mode structures indicating the importance of spatial overlap.