Decentralized molecular detection of pathogens remains an important goal for public health. Although polymerase chain reaction (PCR) remains the gold-standard molecular detection method, thermocycling using Peltier heaters presents challenges in decentralized settings. Recent work has demonstrated plasmonic PCR, where nanomaterials on a surface or nanoparticles in solution heat upon stimulation by light, as a promising method for rapid thermocycling. Heating of a solution via nanoparticles suspended in solution has been demonstrated in PCR tubes, but not on microfluidic chips. We developed a volumetric, microfluidic plasmonic reverse transcription (RT)-PCR method. A microfluidic chip is fabricated with an integrated thermocouple to measure internal temperature, feeding into a proportional-integral-derivative (PID) algorithm that modulates an infrared LED for closed-loop control. Gold nanorods are dispersed in solution with RT-PCR reagents. We created an instrument for plasmonic RT-PCR using an infrared LED for heating, fan for cooling, and fluorometer for end-point fluorescence detection. Rapid thermocycling and amplification of SARS-CoV-2 within 16 min (5 min for RT, 45 cycles in 11 min) is achieved. This paper demonstrates volumetric, plasmonic PCR in a microfluidic chip, using an integrated thermocouple for closed-loop control. This work points to the promise of using microfluidics and nanomaterials to achieve rapid, compact detection of pathogens in decentralized settings.