The dark exciton state strongly affects the optical and quantum optical properties of flat InP/GaInP quantum dots. The exciton intensity drops sharply compared to the biexciton with rising pulsed laser excitation power while the opposite is true with temperature. Also, the decay rate is faster for the exciton than the biexciton and the dark-to-bright state spin flip is enhanced with temperature. Furthermore, long-lived dark state related memory effects are observed in second-order cross-correlation measurements between the exciton and biexciton and have been simulated using a rate-equation model.