Discrete emission lines from self-assembled InGaAs quantum dots (QDs) grown in the submonolayer (SML) deposition mode have been observed in micro-photoluminescence (PL) spectra at 10K. For the first time, the SML-grown InGaAs/GaAs QD heterostructure is verified to be a quantum-dot-quantum-well (QDQW) structure, by using high power PL and selective PL with excitation energies below the band gap of the GaAs barriers and temperature dependent PL. As the temperature is increased from 10 to 300K, a narrowing of the full width at half-maximum at intermediate temperatures and a sigmoidal behaviour of the peak energy of PL band of the SML QD ensemble are observed and attributed to thermally activated carrier transfer between QDs via QW states.