Ultrafast differential transmission spectroscopy is used to explore temperature-dependent carrier dynamics in an InAs/InGaAs quantum dots-in-a-well heterostructure. Electron-hole pairs are optically injected into the three dimensional GaAs barriers, after which we monitor carrier relaxation into the two dimensional InGaAs quantum wells and the zero dimensional InAs quantum dots by tuning the probe photon energy. We find that carrier capture and relaxation are dominated by Auger carrier-carrier scattering at low temperatures, with thermal emission playing an increasing role with temperature. Our experiments provide essential insight into carrier relaxation across multiple spatial dimensions.