cartridge heater control
This is kind of a broad question. Usually time proportioning systems are used with cartridge heaters, with time bases of tens of seconds and the system acts as a low pass filter. You can go a bit faster with an SSR. 

A temperature control is conceptually simple- measure the temperature (PV) from a sensor, signal condition and convert to digital if required, feed the PV and the setpoint (SV) into a controller algorithm and get the output and run the output actuator, plus display the PV/SV or whatever else you want to do. The details can be complex. 

For overtemperature safety you should endeavor to use something of different technology and as simple as possible. For example, a resettable trip thermostat or a simple mechanical thermostat. Consider that the SSR may (will probably) fail shorted at some point in the future. If injury or significant material damages are possible, great care needs to be taken. 

You can buy modular temperature controllers and many industrial control loops use such modules, either discrete, or as part of PLCs or other control equipment.