Not sure whether you have the early 2005 or the late 2005 model, but the general construction of the CPU/heatsink assembly, as
@Certificate of Excellence noted, are discrete units for each physical CPU. You likely know this already, but there are very helpful guides on iFixit for both the
A1047 (early 2005) and
A1117 (late 2005) editions.
Having done a thermal paste refresh on my A1047 a couple of times, there is a crucial chip which are two crucial chips found on the U3/Backside of the main board. Getting to these takes a bit more work, finesse, and patience, but keeping those chips cool may be as important, if not more so, than keeping the CPU(s) cool.
If you do go through with it, the main chip of concern on the backside is the memory controller. This has a
long track record of failure, mostly due to overheating and also the quality of the solder joints used in board assembly. My own A1047, even after new thermal paste, can still hot enough to do a thermal protection shut down, though this was alleviated somewhat by harmonizing all RAM sticks from the same maker, same specs, bought together.
If you do a backside thermal re-paste, you also find a lot of long-hidden dust and grime accumulation along the main cooling route (easier to see than to explain, but will be obvious to your eyes once you do). This also gives you the opportunity to clean the fans both next to the hard drive slots and also
behind the slots. (This latter one is the constant-speed fan used to route cool air through the backside.)
And while you’re in there, a careful removal, opening, and blowing out of dust from the power supply and its two fans will help to keep things cooler in there, as finding these uniquely-shaped power supplies nowadays, when they do fail, is getting tough.