Say that a 10deg proportional band gives you the tight, stable control that you want after the process has settled down but power throttles back too late to avoid overshoot on start up. You could design the controller to introduce a pause at say 30 deg before set point. That is, move the proportional band temporarily downwards 30 deg. The controller now throttles back the power that much sooner, then slowly takes the proportional band upwards to its normal position. Note that this parameter name and means of implementation varies with manufacturer.
Self tuning Many controllers have a feature called self-tune or automatic tune.
Upon initiation the controller typically gives a controlled dose of heat to the process and from the temperature response back from the process, calculates optimum settings for the PID parameters and sometimes other parameters. Record these after a successful self tune. Self tuning can take anything from a minute or two in the case of a fast tungsten lamp applying heat to a low mass material to one hour or more with a slow, large mass process. It is advisable to start self tune when the process is at or a bit lower than its normal working temperature. Watch the temperature at this stage and be ready to intervene if the initial heat dose threatens to overheat your material or equipment.