A really good way to tell is to consider the relationship between your input and output. PID get's thrown around all the time because a lot of the time you are talking about controlling an accerlation (gas pedal, throttle) to effect a position, so you theoretically need a PID to stand in for a 2nd order differential equation since position and acceleration are two derivatives apart with respect to time. But as you pointed out, you usually can generalize your input and not worry about the D term.
In the video game I'm making, I don't really worry about derivative control, but PID control is mostly there to give the illusion that someone is driving a vehicle rather than it be controlled perfectly by a computer program. I don't want to model out how "skilled" the driver is - all I have to do to give that impression is just give the vehicle better handling.
With a heater,once you get to zero error, any overshoot will reduce back the opposite way because heat is always lost.
Of course, a "perfectly" tuned PID loop will be "better" - more efficient, faster to reach setpoint, and minimize overshoot. But the effort/engineering time/operation time involved in tuning it, combined with the risks presented by a subtly poorly tuned loop that goes haywire one day when the system paradigm (characteristic) changes...just isn't worth it.
Obviously there are times when you really do need a D term, but I can confidently say that they're not commonly used in HVAC or petrochemical plants. I'm sure there are other domains where the D term is needed, but in my time as a controls engineer I didn't run across them.