Summary: Radial (or circular) cooling fin is an extension of a cylindrical surface widely used to increase the rate of heat transfer from the heated surface to a surrounding cooler fluid. The only type of radial fins for which an exact closed-form expression for the one-dimensional temperature distribution is available in the literature is radial fins of constant thickness. In this article, we discover a new family of radial fins for which the temperature distribution along the fin can be computed in closed form. The profile curve of the new radial fin satisfies a non-linear, non-autonomous ODE and, depending on the initial condition and the sign of the right-hand side of the ODE, can have three distinct geometric shapes. We found that partial-length novel radial fins described in this work have the following equivalence property: If the ratio, \( \sigma\), of the heat transfer coefficient on the fin’s tip to that on its lateral surface is not too large (specifically, satisfies inequality (39) in Sect. 7), then the temperature distribution within a fin with a non-adiabatic tip is identical to that for a longer fin with adiabatic tip. Our analysis of heat transfer by radial fins is only based on standard homogeneity, steady-state and one-dimensionality assumptions. In particular and most importantly, we dispensed with the “length-of-arc” assumption that underlies most of the previous work on heat transfer by radial, straight and pin fins. Although the analytic form of the temperature distribution for the family of radial fins discovered in this work is remarkably similar to that for the families of straight and pin fins found in [the first author and D. E. Brown, ibid. 119, 93–114 (2019; Zbl 1437.34059)], the geometries of these fin families are strikingly dissimilar.