We report on kilohertz-repetition-rate flame temperature measurements performed using blue diode lasers. Two-line atomic fluorescence was performed by using diode lasers emitting at around 410 and 451 nm to probe seeded atomic indium. At a repetition rate of 3.5 kHz our technique offers a precision of 1.5% at 2000 K in laminar methane/air flames. The spatial resolution is better than 150 m, while the setup is compact and easy to operate, at much lower cost than alternative techniques. By modeling the spectral overlap between the locked laser and the probed indium lines we avoid the need for any calibration of the measurements. We demonstrate the capability of the technique for time-resolved measurements in an acoustically perturbed flame. The technique is applicable in flames with a wide range of compositions including sooting flames.