This study investigates changes to the Madden-Julian Oscillation (MJO) in response to greenhouse-gas induced warming during the 21st century. Changes in the MJO's amplitude, phase speed, and zonal scale are examined in five Coupled Model Intercomparison Project Phase 5 (CMIP5) models that demonstrate superior MJO characteristics. Under warming, the CMIP5 models exhibit a robust increase in the spectral power of planetary-scale, intraseasonal, eastward-propagating (MJO) precipitation anomalies (~10.9 %K-1). The amplification of MJO variability is accompanied by an increase of the spectral power of the corresponding westward traveling waves at a similar rate. This suggests that enhanced MJO variability in a warmer climate is likely caused by enhanced background tropical precipitation variability, not by changes in the MJO's stability. All models examined show an increase in the MJO's phase speed (1.8 - 4.5 %K-1) and a decrease in the MJO's zonal wavenumber (1.0 - 3.8 %K-1). Using a linear moisture mode framework, this study tests the theory-predicted phase speed changes against the simulated phase speed changes. It is found that the MJO's acceleration in a warmer climate is a result of enhanced horizontal moisture advection by the steepening of the mean meridional moisture gradient and the decrease in zonal wavenumber, which is partially offset by the lengthening of the convective moisture adjustment timescale and the increase in gross dry stability. While the ability of the linear moisture mode framework to explain MJO phase speed changes is model dependent, the theory can accurately predict the phase speed changes in the model ensemble.