For every intermediate control output there is some stable temperature. Generally we don't know the shape of this curve. Suppose we want to control the temperature to a setpoint, indicated by the horizontal green line, labeled Set Point. The darkened band shown is the Proportional Band. The system will eventually stabilize at temperature T2, since that is the point at which the system response line intersects the controller output.
Proportional controllers are simple, but they are likely to result in an offset.
Also, since the viscosity of a liquid is decreased by the addition of heat or a solvent , the system response line slopes down with increasing control output. The figure below illustrates an initial setting with PI viscosity control. The black line represents the system response to either adding heat or solvent. The graph illustrates the system in its initial state with an offset. If it is below the proportional band is very slowly adjusted upward at a rate that is slow compared to the response time of the system.