Is there a metal that melts and solidifies quickly? Is there any kind of metal that melts very quickly with very low heat or temperature, and at the same time, becomes hard very 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.