The MDD is actually designed to shut down as it approaches the overheat stage. There is a temp sense circuit that controls this. Unfortunately, it doesn't give any on screen warning, nor does it do a graceful shut down. It simply dies, as if you pulled the plug. Obviously that can create problems.
As you and most of the posts here have indicated, the machine is also extremely prone to getting too hot.
The engineers did a VERY poor job of managing heat generation and airflow with the MDD. Too many components, in too small of a space, with too little venting.
They allowed their desire for a "coolness" factor to overtake engineering robustness and the machine obviously did not get enough testing before going into production, and the "fancy cool vents" on the bottom of the front are a joke, and only inhibit air flow instead of helping it.
And this doesn't even mention the loud original Wind Tunnel P.S.
The airflow, what little there is, and the geometry of the items inside the case also results in a massive buildup of dust, in a relatively small period of time, depending on the quality of air cleanliness in your house.
I like the idea of redoing the thermal grease. After this many years, most of these cpu chips probably have very dried out, thus ineffective original paste.
As an aside, I will mention that a couple years ago I got tired of opening the door and finding the whole insides sludged up with dust, and also with the van noise (I never got the replacement fan).
So I ended up totally opening and discarding ALL of the original housing, except for the sheet the logic board is mounted too. I now run the entire system with the main board (with alum backing) laying on my desk, and with all the drives and opticals just laying around on the desk. I have three extra fans I placed on and around the components, especially a large one on top of the main heatsink, and a smaller one for the hard drive.
I use SCR based lamp dimmer rheostats to adjust each of the fan speeds.
I blow the heck out of it every week just to keep all the pieces as clean and "non dust covered" as possible.
The whole machine runs very cool now (I use Temperature Monitor).
Unless I forget to turn all the fans on before I start the machine up ;)