Motivated by recent experimental results, we present a detailed account of adiabatic population transfer in InGaAs/GaAs quantum dots by strong chirped laser pulses. Specifically, numerical simulations in very good agreement with experimental results allow for a clear physical picture of this process. An analytical expression is developed, which is used to analyze the strong-field adiabatic population transfer in the presence of the phonon environment. Optimal pulse parameters to achieve robust population transfer at temperatures as high as 80 K are identified and are confirmed by numerical simulations.