We study the photoluminescence and impact of post-growth annealing of stacked, strain-free GaAs quantum dots fabricated by refilling of self-organized nanoholes using molecular beam epitaxy. Temperature- and power-dependent photoluminescence studies reveal an excellent optical quality of the quantum-dot stack. After high-temperature post-growth annealing only slight blueshifts and an increase in full width at half-maximum of the photoluminescence peak are observed, indicating very high-temperature stability and crystalline quality of the stacked GaAs quantum-dot structure.