Here is the relay:
NTE RS3-1D40-21 http://www.alliedelec.com/search/productdetail.aspx?sku=70011919
I wanted to use this relay to take pwm input from my arduino and then have the relay control however much power is need. I want to be able to control how hot the element gets with pwm. I'd like for the Arduino to measure this and be able to switch off the relay before it gets too hot.
PWM and AC solid state relays don't go together too well, if at all, because you are endeavouring to switch an AC power circuit, whereas PWM is designed for switching DC circuits. Your best bet is to "burst fire" the relay whereby it is turned on for several cycles or seconds, then turned off. For example, if you require only 1/3 heating effect, you turn on the relay for say 5 seconds and then turn it off for 10 seconds; this is the equivalent to 33% PWM. How long you set the ON and OFF periods depends on how responsive your control system is to the thermal inertia of the system being heated.
Most industrial heating controllers operate on the principle of "burst firing".
I agree with jackrae.
The reason in more detail (as I see it). The PWM on arduino runs at about 500 cycles per second. The AC line runs at 50 or 60 cycles per second.
The SSR for AC loads, switches at 50 cycles per second, while your PWM is assuming the load switching 500 cps.
The burst fire method that jackrae describes will be much better, and predictable.
As others have said, you should use burst-fire control for a heating element, which is like very slow PWM. You can generate a very slow PWM signal either in software, or from a 16-bit timer in the Arduino (timer 1 if you are using a Uno).
The relay you have linked to is of the random turn-on type, which is better suited to switching inductive loads than heating elements. Look for a zero-crossing SSR instead. This will generate less interference on the mains. Maybe type SSR-40DA, which is widely advertised on eBay.
Depending on the current drawn by the heating element, you may need a heatsink for the SSR.