Analog PID and high power
Feed the control output into a PWM with a period of a few seconds and control an SSR (solid-state relay) with it. That's standard practice for industrial temperature control loops. Most likely you will be using mains power for the heater.  

Boilers are potentially extremely dangerous, so you need fail-safe measures to ensure an explosion is impossible. At a minimum, I would think, a pressure relief valve and an over-temperature cutout, in addition to the controller, but it's up to you to evaluate all of the safety aspects.  

Also note that your PID controller is too simple to work well, it lacks anti-reset windup provisions, so it will tend to overshoot greatly. It also needs to be tuned to the system dynamics (at least two degrees of freedom, and potentially three), or it will almost certainly be sluggish, over/undershoot or oscillate.