yeah, one limit of the PID controller is that it pretty much just operates on current values. You could, I suppose, create a predictor algorithm to feed into the PID control... but I wouldn't bother. If you're going to that much trouble, you're better off designing a proper discrete time controller to do the whole shebang.
Also, you will find that this system will probably be fairly slow to react anyway. There's a lot of thermal inertia involved when dealing with water, particularly that quantity. It will take a long time to show a reaction to your inputs. For this reason, I wouldn't have thought that you'd need to average out any readings. When you do that, you're effectively slowing down the speed at which you can take readings, by introducing a low pass filter (averaging algorithm). With all that thermal inertia and slowly changing values (within reason), I don't think there'd be any need for that.
Another reason that I will steer clear of PID is that with a proper discrete controller, you can account for the frequency that you can take sensor readings, calculate control values, set control... and lag in the system regarding readings, etc... but again, that's quite advanced and probably overkill. But as far as I'm concerned... no half measures
And you're right about overshooting, it's probably not a huge deal. Just keep an eye on it, and define BEFORE YOU START what an acceptable overshoot is. If you do that later, you'll just get lazy and end up with a 10 degree overshoot (trust me, I've been there...) If you're after a quick ramp time, you'll always end up overshooting. Whether or not you start oscillating or not is another matter. Just be aware that the faster you try to ramp, the more you'll overshoot, and the more likely you'll set up oscillations. I usually aim for the "critically damped" result - the fastest possible response without overshooting.
And go take your measurements. They will provide valuable insight into your system - how you need to set up your sensors, how the system behaves and reacts, etc... Any more questions and I'll be happy to answer (or at least try to
). Control theory is one of my things. Microcontrollers is another.