Quantifying the amount of heat transfer between a micro-surface and its environment is essential in the design of many micro-devices. The present study investigates the transient heat conduction through a gas between two cylindrical surfaces in order to gain some insights. An analytical solution of a temperature-jump model can be helpful but analytical investigation of the time-dependent temperature-lump models is not easy even for a simple one-dimensional geometry. Therefore. this study employs the Heaviside operational method to solve a second-order temperature jump model. The study gives a generalization of the Heaviside expansion theorem and a semi-analytical procedure for using it. Then it solves the variation of gas temperature with time and with distance from a cylindrical micro-surface and examines the amount of the temperature-jumps at curved surfaces.