The performance of heat pipes with localized heat input including the effects of axial and circumferential heat conduction under high and low working temperatures is investigated. The numerical results show that when heat pipes are spot heated, the peak temperature of the wall is greatly reduced and the surface can be protected from being burned out by the high heat flux. The boiling limitation becomes the most important limitation for this type of heat pipe. Numerical results for block heating a heat pipe with low working temperatures indicate a good agreement with existing experimental data. It is also shown that most of the input heat passes through the wall beneath the heated block.