Your understanding is wrong. PWM (called time proportioning in the industry) is actually commonly used with mechanical relays. Naturally the period would be closer to a minute than the few seconds that is possible with a SSR or less than the milliseconds equivalent speed of a phase control.
How often you have to sample the temperature error is (almost) unrelated.
What matters with sample rate and output timing is the characteristics of the system you're trying to control and how far from optimal control you're willing to live with.
If the system does not change "too much" in temperature in 30 seconds you can use a 30 second PWM period. Your sample time and PWM output period (roughly speaking) act as dead times in the feedback control. Dead time can be nasty for good control but not a problem if it is much less than the slowest lag in the system. Some systems are happy with time proportioning control (your home thermostat works like that), some require faster period, some require phase control, and some require more like a servo DC output (even for temperature control). Horses for courses.
Even if the system responds relative quickly, it's possible to sample more slowly by detuning the system (making the controller the slowest lag in the system) but of course the output cycling itself must not cause excessive errors in the controlled variable.