Temperature measurements at the nanoscale are vital for the application of plasmonic structures in medical photothermal therapy and materials science but very challenging to realize in practice. In this work, we exploit a combination of surface-enhanced Raman spectroscopy together with the characteristic temperature dependence of the Raman peak maxima observed in β-phase copper phthalocyanine (β-CuPc) to measure the surface temperature of plasmonic gold nanoparticles under laser irradiation. We begin by measuring the temperature-dependent Raman shifts of the three most prominent modes of β-CuPc films coated on an array of Au nanodisks over a temperature range of 100-500 K. We then use these calibration curves to determine the temperature of an array of Au nanodisks irradiated with varying laser powers. The extracted temperatures agree quantitatively with the ones obtained via numerical modeling of electromagnetic and thermodynamic properties of the irradiated array. Thin films of β-CuPc display low extinction coefficients in the blue-green region of the visible spectrum as well as exceptional thermal stability, allowing a wide temperature range of operation of our Raman thermometer, with minimal optical distortion of the underlying structures. Thanks to the strong thermal response of the Raman shifts in β-CuPc, our work opens the opportunity to investigate photothermal effects at the nanoscale in real time.