Purpose The purpose of this paper is to study an expandable or contractible metallic fin and heat transfer process. The fin is assumed to be thin having a rectangular cross section. It is attached to a hot surface with a time-dependent temperature, and its tip extends to a medium (fluid) of an ambient temperature. With the insulated wall constraint at the tip, the tip of the metallic fin has the property of expanding or contracting in time at a specific rate. Design/methodology/approach The corresponding physical problem is so formulated that the unsteady heat transfer problem is governed by means of a similarity variable represented by a second-order ordinary differential equation. The system can be reduced to the traditional well-documented steady state fin problem often studied in the literature, if the unsteadiness is turned off from the formulated system. Findings The system is then solved analytically for the temperature distribution through the fin. The fin tip temperatures are calculated, and the heat transfer analysis is made with varying physical parameters. And finally, observations are discussed leading to better fin efficiency and heat transfer enhancement. Originality/value An expandable or contractible metallic fin and heat transfer process are analyzed for the first time in the literature. Full solutions are presented, whose numerical correspondence is discussed through graphical and tabular forms.