I'm not sure, though I know there are some specific heat considerations for building materials, etc. I suppose an electrical fuse needs to have low specific heat in order to melt, but it already needs to be a metal to conduct the electricity anyway. I'm really not sure about any other specific uses, most of the situations I can think of already require the use of metal for another reason.
The heat capacity of metals per mole is not particularly low (this is due to the Dulong-Petit law), many of them just have a high molar weight, so the heat capacity per mass is lower. It is useful because you need to heat iron for example to 1540 °C to melt it.