Specific heat measurements were made between 0.4 and 3.0 °K. For rubidium (nominal purity 99.9%, actual purity probably ~ 99.99%) the electronic specific heat coefficient γ is 624.6 ± 6.5 μcal/°K2 g atom and the low temperature limiting value of the Debye temperature (ΘOoc) is 56.5 ± 0.2 °K. For cesium (nominal purity 99.99%, actual purity probably ~ 99.97%) γ is 950 ± 20 μcal/°K2 g atom and ΘOoc is 40.5 ± 0.3 °K. These Debye temperatures are in fair agreement with ΘOoc1 values calculated from low temperature elastic constant measurements. Electron effective masses (calculated from γ) are 1.37 ± 0.01 for Rb and 1.80 ± 0.04 for Cs. Thermal effective masses for all the alkali metals are compared with recent theoretical results. Sample purities were checked by an independent spectrographic analysis and by making a thermal analysis in the melting region on the actual specific heat samples. These thermal analysis results led to a review of earlier work on the melting of these metals and the following revised values of melting point and latent heat of melting were obtained: Rb: 312.47 ± 0.02 °K, 524.3 ± 1.0 cal/g atom; Cs: 301.67 ± 0.13 °K, 501.0 ± 1.0 cal/g atom.