We describe the onset of plasma instability due to heat conduction in a fully ionized hydrogen plasma with small temperature, pressure, and electric potential gradients. The effect of these gradients on plasma stability depends on a single inhomogeneity parameter Bt, which is a measure of the ratio of the electron mean free path to the scale height of the plasma. A large value of ‖Bt‖ indicates that the plasma is collisionless. We find the least value of ‖Bt‖ needed to produce instability for the range of electron to hydrogen ion temperature ratios T and ion to magnetic pressure ratios &bgr;i, relevant to the solar wind and other plasmas. The wave parameters of the first unstable modes (the modes which become unstable for the least value of ‖Bt‖) are described. The fast mode is the first unstable mode at high &bgr;i, the intermediate mode is the first unstable mode at low &bgr;i, and low temperature ratios, and the slow mode is the first unstable mode at low &bgr;i and higher temperature ratios.