Chosen Solution
Within the fan is a tachometer to monitor the fan’s RPM (feedback) that way the SMC logic can make sure to set the fan as the correct cooling level needed. The error PPF003 really doesn’t tell us if the fan its self or the controlling logic is the problem. The easiest way is just replace the fan to see if that solves the problem or not. MacBook Air 13" (Late 2010-2017) Fan and here’s there guide to put it in MacBook Air 13" Mid 2013 Fan Replacement. I would first get a soft paint brush and a can of can’ed air to clean the dust and debris thats collected inside out. Your fan may every come back to life! You may want to use a better way to monitor your systems thermals, I like this tool TG Pro