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• Presents an analytical solution for thermal spreading in a cylindrical body with spatially varying side wall cooling. • A series solution is derived, with coefficients shown to be the solution of a set of linear algebraic equations. • Impact of key non-dimensional parameters on temperature field and thermal resistance is investigated. • Results are shown to be in excellent agreement with past work for special cases. • Results are of relevance for edge cooling of microprocessor chips as well as batteries. Thermal spreading and constriction resistance play an important role in thermal management of a variety of engineering systems, including semiconductor devices. Moreover, thermal contact resistance at interfaces between materials is also governed by spreading and constriction processes. Most of the past literature on theoretical modeling of thermal spreading from a source into a larger body assumes an adiabatic side wall, whereas several recent thermal management problems involve active cooling at the side wall. This work addresses such scenarios by solving the thermal spreading problem in a finite thickness cylinder with spatially varying convective heat transfer on the side wall. An eigenfunction-based series solution for the temperature field is written, the coefficients of which are shown to be governed by a set of coupled algebraic equations. Results are shown to agree well with past work for special cases of the general analysis presented here. Thermal spreading resistance is computed for a number of practical scenarios, including step function, periodic and sinusoidal convective cooling on the side wall. In each case, it is shown that the temperature distribution is consistent with the nature of the spatially varying boundary condition. A key theoretical insight from this work is that under certain conditions, the classical definition of thermal spreading resistance may become negative due to the presence of two heat sinks in the problem. Therefore, analysis based on total resistance may be more appropriate. This work offers a significant generalization of past papers, making it possible to analyze realistic thermal management problems, in which, side wall cooling plays an important role. [ABSTRACT FROM AUTHOR]