Is there a metal that melts and solidifies quickly?
The melting points of some eutectic mixtures are tabulated in an article by French.1 Some options for low-melting point metals/mixtures are:


Gallium-indium eutectic, mp 15.7 °C (Sigma-Aldrich catalogue)
Galinstan, mp –19 °C (Wikipedia article)
Various gallium-based Indalloy® alloys, mp between 7.6 and 29.78 °C (corporate page)
A general search for "fusible alloys" brings up several sources with many choices:


Wikipedia page
Rotometals sales page
Belmont sales page
Bolton Metal sales page





Reference


French, S. J. Melting Points of Eutectics. Ind. Eng. Chem. 1936, 28 (1), 111–113. DOI: 10.1021/ie50313a026.