The temperature dependence of the differential gain in AlInGaAs 1310-nm vertical-cavity lasers is investigated. The variations in differential gain and in relaxation resonance frequency are shown to depend on the room-temperature offset between the gain peak wavelength and the wavelength of the lasing mode. The tradeoff between high modulation bandwidth and good high-temperature performance for vertical-cavity lasers is analyzed. A cavity mode that is red-shifted about 25 nm from the gain peak is shown to minimize the variation in modulation bandwidth with temperature, and simultaneously allow for satisfactory high-temperature operation. Experimental results are presented and compared to calculated results with excellent agreement. Because of the change in gain-mode offset with internal temperature, the measured modulation current efficiency changed from about 2 to 4.8 GHz/mA/sup 1/2/ for an increase in drive current from 2 to 10 mA.