........... snip..........Would having a "heat shrink" in the form of a slab of ham in there make a difference? My gut feeling is not.
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I think the word you're looking for is "heat sink" which is simply something that absorbs heat. That is frequently something like a piece of aluminum clamped to a component which gets hot to help with dissipating potentially damaging heat. In other words, a heat sink is simply a set of cooling fins in many cases. Chances are the processor inside your computer has one. Heat sinks are generally not made from ham. The chilled piece of steel (called an enswell) a cutman holds against the swollen eye of a boxer between rounds is also a heat sink designed to slow the local blood flow and reduce the swelling.
However, I think what you really want to discuss is the effects of a "thermal mass". This is something (like a ham) which will absorb and hold heat. A feather pillow has a low thermal mass while a cast iron engine block has high thermal mass.
The idea of a PID controller is simply to have a way to adjust the power to a heat source which is more sophisticated than a simple on/off relay. A simple relay triggered by a particular set point will always overshoot the target temperature. But a PID controller has a "brain" which can anticipate when you approach a set point and reduce or turn off the power ahead of time to reduce or eliminate overshoots.
As you might imagine, if your BBQ were made of thin steel without insulation and weighed around 5 pounds, then it would have a very low thermal mass. Heating it up and cooling it off would happen very quickly. On the other hand, a heavy, thick-walled ceramic cooker would take a while to heat up and cool down. The PID settings for the two units would be quite different. So we experiment with our BBQ rigs and our PID controllers in order to fine tune the PID settings to get stable holding and reasonable overshoots. A well tuned PID system will normally overshoot the set point a little bit because that lets the system reach the set point more quickly. If you tune for no overshoot at all, the system will take forever to "creep up" on the desired temperature, so we normally accept some reasonable amount of overshoot.
Now let's consider the ham. Since it adds thermal mass to your system, it WILL make a difference in your PID settings, so ideally you would fine tune your cooker with a representative chunk of food in there along with a proper sized fire. For example, when I was breaking in a new ceramic cooker a few weeks ago, I burned a small fire at low temperatures for quite a long time. I tried tuning the PID settings and had some success, but the fire was so small and the temperature low enough that the results were not ideal. Later on I had to adjust them when I was cooking chicken at higher temperatures.