The junction temperature rise may not only affect its output power, slope efficiency, threshold current and lifetime, but also will cause the spectral broadening and wavelength shift in a high power semiconductor laser. Therefore, thermal management becomes one of the main problems in research and development of pump laser. In this paper the physical model of the noise power spectrum and junction temperature variation is first established; according to the compression sensing theory, and after sparsing the measured aliasing composite noise signal containing Gaussian white noise and 1/f noise, the basic pursuit denoising algorithm is used to do denoising; through changing the iterations times of the used algorithm and the size of measurement matrix, the curves of the ration between noise voltage power spectrum and junction temperature variation are obtained, thereby avoiding the complexity of direct measurement of the junction temperature. The numerical estimation results can better guid us in doing the thermal management work in high power semiconductor lasers.