Hi, Closed loop control is an imprecise science, there's always some uncertainty in terms of your 'plant', but also the requirements. We don't have any idea of how precise your control needs to be, that's not a problem, I spent 4 decades designing control systems and very rarely came across a rigorous performance specification.
If as you say, your time constant is going to be small, then on-off control could be troublesome. PID (you may not need the D, and it's a lot easier without it) with PWM on your heater could give you better results but if this is new to you you'll find it quite an exercise. Maybe try on-off first, which can be implemented more easily. Just one more thing, on-off schemes often incorporate some hysteresis. Plenty of info on the web.
Enjoy