Don't see why the RTD wouldn't work. Although you can get beefier ones from China:
RTD PT100 Temperature Sensors with Terminal Head | eBay
As for the PID, like P-J says, it's relay output, not SSR output, (so you'll need a transformer to step the voltage from 120VAC to 3-32VDC to control your SSR). It reads in Centigrade, not Fahrenheit. It says it only takes a K type thermocouple, (which is NOT an RTD and isn't as sensitive, but is cheaper usually). It doesn't mention if it's capable of autotuning, (which is very useful for a newbie). It also doesn't appear to have a manual mode, (damn near essential if this will be controlling your BK). Finally, it's a good bet that the manual is in very bad english, seeing as it's a chinese import and looking at the english level of the ebay post.
I cheap out on a lot of stuff and buy from China. The PID is one thing I'm very glad I bought from Auber. Get the 2352. It has SSR output, takes an RTD, has a bumpless manual mode that's easily accessible, reads in F, has autotune, and it's decently documented.
Edit: Whups, didn't see Protto's post above. Apparently it does do Fahrenheit and can take RTDs. Still, I vote Auber. Manual mode is very useful.