The attachment of fins to a surface may significantly enhance the heat flow rate by convection from that surface. The aim of this paper is to review and investigate analytically the two-dimensional, time-dependent heat transfer in extended surfaces. Both fins in isolation and fin assemblies, where an array of fins is attached to a supporting wall, subjected to periodic variations in temperature, are considered. A comparison is made of one- and two-dimensional solutions for each problem. The effects on the heat flow rate produced by the oscillatory parameters, the heat transfer coefficients and the fin or fin assembly dimensions are investigated, in order to gain a better understanding of the performances of heat exchangers under transient conditions.