Re-building a Crock-pot controller - how are the heating elements powered?
I can think of a number of ways to answer your question.  One source of information might be a service manual (if one is available), but perhaps an even easier source of information is the US Patent Office.  For example, US patent 6573483 is a patent for a slow-cooker accessory that shows both a thermistor and a triac for controlling the heating element.  That particular patent is rather light on details, but you might look at the referenced patents for more information if you need it.
As for details, triac manufacturer application notes are likely a good source of information for redesigning this circuit.  In particular, you may find Power Control with Thyristors and Triacs from NXP useful for this purpose since it describes not only the basics of triac operations, but also a specific section titled &quot;Design of a Time Proportional Temperature Controller&quot; describes a control algorithm that is likely to be of interest.
Finer control of the temperature, including temperature ramp and tight regulation, might be an application worthy of throwing a microprocessor at it!
Update
I would be skeptical of the version 1 module mentioned in the comments, but it appears that some of the problems are address in version 2, including making the traces on the PCB wide enough for the expected current.  Before proceeding too much farther, it would make sense to measure the AC current used by the heating element and/or seeing if there are markings on it indicating the current.  Since the original triac was rated for 8A, I would be cautious about substituting one with a significantly lower current rating (as with the BT136S that comes on that module.)