We characterize the frequency-sensitivity of a cavity-stabilized laser to inertial forces and temperature fluctuations, and perform real-time feed-forward to correct for these sources of noise. We measure the sensitivity of the cavity to linear accelerations, rotational accelerations, and rotational velocities by rotating it about three axes with accelerometers and gyroscopes positioned around the cavity. The worst-direction linear acceleration sensitivity of the cavity is $2(1) \times 10^{-11}$/g measured over 0-50 Hz, which is reduced by a factor of 50 to below $10^{-12}$/g for low-frequency accelerations by real-time feed-forward corrections of all of the aforementioned inertial forces. A similar idea is demonstrated in which laser frequency drift due to temperature fluctuations is reduced by a factor of 70 via real-time feed-forward from a temperature sensor located on the outer wall of the cavity vacuum chamber.