5-Speed manual 2001 Toyota Celica GT

When my 2001 Toyota Celica GT is at full operating temp, after a bit of driving (10+ miles) my idle gets super rough and will sometimes stall out. Alongside, when I’m driving, my throttle response stops and I can put pedal to the metal, but my car will gradually slow down until it stalls while I’m rolling. What I’ve do to counter that is turn the car off and let it sit for a while and continue the drive. What could this be caused by? I’m assuming my IAC valve is part of it but I’m unsure what else.