Increasing power density (due to faster clock and high device integration density) coupled with limited cooling capacity of the package causes die overheating and leads to reliability concerns. In this paper, we present a methodology to mitigate temperature-induced reliability problems by transferring the heat dissipated in a region of high activity (such as the ALU in a processor that creates localized "hotspot") to regions of lower activity (such as on-chip cache). We propose to use carbon nanotubes (CNTs) as "thermal interconnect" for on-die heat transfer since CNTs have significantly higher thermal conductivity than typical heat-spreader materials. We note that the proposed heat transfer framework is particularly suitable to thermal management in silicon-on-insulator (SOI) devices, which suffer from fine-grained thermal gradient. Simulation results indicate that the use of CNTs for heat conduction from hotspot to a region of lower activity (which we denote as a 'coolspot'), achieves 13% (16degC) decrease in temperature at the hotspot and only 3% (1.5degC) increase in temperature at the coolspot of an alpha microprocessor model.