arduino PWM temperature inexpected results
As Gerben said in a comment, you should add the value of Input to the serial print, to facilitate problem diagnosis.  As your question stands, one can only speculate about what the problem might be.  My speculation is that the system is unable to cope with parameters (Kp, Ki, Kd) = (0, 20, 20), ie, that it's unstable and unresponsive without proportional control.