The instabilities produced by a linear model of the tropical atmosphere coupled to a prognostic equation for water vapour are investigated. For parameter regimes relevant to the Indo-Pacific warm pool, the long-time asymptotic behaviour of the unstable waves is found to be absolutely unstable, so that the amplitude of disturbances will grow in time at every point in the domain. Other limits of the system do not produce this same behaviour at these length and time scales. It is shown that the resultant long-time behaviour of the instability is characterized by roughly equal roles for temperature and moisture fluctuations in setting the thermodynamic tendency of the waves. Under the assumption of a zonally varying flow, it is shown analytically that localized regions of instability may be formed, again using parameter choices relevant to the warm pool. The dynamics and thermodynamics of these local instabilities show some correspondence with the observed development of the Madden-Julian Oscillation as it propagates through the warm pool.