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The dynamics of injection-locked vertical-cavity surface-emitting lasers (VCSELs) are studied as a function of temperature. The temperature dependence of the slave VCSEL's parameters is used in a rate-equation analysis and parametric maps in the injection strength K- and frequency detuning ω-planes are calculated in order to investigate the temperature dependence of the system's stability. We demonstrate that, as we increase temperature for the range where the linewidth enhancement factor α starts to stabilize, approximately 10 K above the temperature of where the minimum of the threshold carrier density occurs, the locking region tends to be suppressed and the nonlinearities to grow due to the increase of the relaxation resonance frequency ωR and the total loss rate Γ0. Below that range, the opposite route is followed due to the enhanced value of the linewidth enhancement factor α, and the results are sensitive to the intraband relaxation time τ. It is finally concluded that, to take advantage of the stable locking region and to avoid the nonlinearities, it is better for the VCSEL device to have a minimum carrier density of 40 K-50 K below room temperature, thus allowing a good operating tolerance in the range ±20 K around room temperature.