The current paper presents the results of an analytical study of steady state heat conduction in a rectangular tube with eccentric hot spots on both the top and the bottom surfaces. The rectangular domain is assumed to be adiabatic on the lateral surfaces and a single or multiple eccentric hot spots can be applied on the top and bottom surfaces. Isothermal, heat flux, or convection boundary conditions can be applied on the hot spots. Because the hot spots are eccentric, the spreading resistance becomes a dominant factor in heat conduction in the tube. The multiple hot spots, multiple layers and combination problems are also studied in the current paper. The solutions can be applied to the thermal management of three-dimensional stacks of electronic devices, the interconnect layers and the thermoelectric devices.