Not sure what you mean, MUCH MUCH longer than a half cycle.
I mean MUCH MUCH longer than a half cylce of the AC. As I tried to explain and illustrate in the other thread, if you run a 1kHz PWM signal with a 50% dutycycle into an SSR it will basically be conducting 100% of the time - not 50% as the PWM signal dictates. If, however, the PWM period would be, say 1000 times longer than the period of the AC half cycle it doesn't matter much WHERE in the AC half cycle that falling edge of the PWM signal occurs (remember that the SSR will keep conducting untill the AC zero crossing), the error will be very small.

Why is it important for the pulse to be longer than a half cycle?
Not the pulse, the period of the PWM signal.

Looking at your illustration it would seem that any positive going pulse would turn on the SSR for the completion of that cycle?
First of all, there are different types of SSR, the illustration asumes a random firing one. Yes, a pulse will turn ON the SSR which will then conduct "on it's own" until the next zero crossing.

So why would you switch on the SSD for only 10 seconds? Why not much longer?
I didn't say that. I said that the period of the PWM signal could be 10 seconds. The output of the PID routine then tells the PWM generator how much of that period the heater will be powered. If the PID determines it needs 100% power then the SSR will be on continously. If the PID determines it needs 25% power the heater will be on for 2.5seconds and off for 7.5seconds. Now, even if the falling edge of the PWM signal occurs right after the AC zero crossing the SSR will only conduct for the remaining of the half cycle (8.333ms at 60Hz mains) which is a very small proportion of the desired 2.5 seconds. But you can easily use a longer period as well if you want.

Or, as Amoque says, use a simple on/off thermostat.

/Henrik.