We demonstrate that the melting points and other thermodynamic quantities of the alkali metals can be calculated based on static crystalline properties. To do this we derive analytic interatomic potentials for the alkali metals fitted precisely to cohesive and vacancy energies, elastic moduli, lattice parameter and crystal stability. These potentials are then used to calculate melting points by simulating the equilibration of solid and liquid samples in thermal contact at ambient pressure. With the exception of lithium, remarkably good agreement is found with experimental values. The instability of the bcc structure in Li and Na at low temperatures is also reproduced, and, unusually, is not due to a soft T1N phonon mode. No forces or finite temperature properties are included in the fit, so this demonstrates a surprisingly high level of intrinsic transferrability in the simple potentials. Currently, there are few potentials available for the alkali metals, so in, addition to demonstrating trends in behaviour, we expect that the potentials will be of broad general use.