We have investigated the temperature stability of the dichroic atomic vapor laser lock laser frequency lock method. We find that, in general, the lock exhibits significant temperature sensitivity, leading to laser frequency drifts as large as tens of MHz/K. However, for certain configurations of the optical elements of the system, this temperature dependence is reduced to below 1 MHz/K. These temperature-independent points can be found across a broad range of frequencies. We present a numerical model that reproduces the general behavior of the system.