Did you change the Idle Calibration or TJ Max values in the RealTemp Options window?
Click on the Defaults button and then click on OK to reset TJ Max to the default value. What does RealTemp show for TJ Max?
These early CPUs run hot. Try enabling C1E if you want to reduce light load power consumption to see if that helps.
The early 65nm Core 2 CPUs are built like tanks. You will have to try really, really hard before you will ever hurt one so don't worry too much about the core temperature. How much MX-4 did you apply? I have always had good results with a small line over top of where the cores are. I prefer that over the pea size method. You can always pull the heatsink and have a look to see how much coverage you have and then try again. While you have the CPU out, put a flat edge across the CPU in both directions from corner to corner and hold it up to a window to see if you can see any daylight. Some of the heat spreaders are concave or convex so the heatsink does not make full contact like it should.
Here's a good picture from Intel of exactly where the cores are underneath the heat spreader.
http://www.intel.com/pressroom/kits/core2duo/pix/core2duo_illus.jpg
With the Intel OEM heatsink I used to run a very similar E6400 reliably up to about 3400 MHz. With a better cooler, it was Prime 95 stable up to 3640 MHz. Here was my entry into the [H]ard OCP database.
http://hardforum.com/showpost.php?p=1031178478&postcount=670
Almost 6 years later and I am typing this message on the same Asus P5B motherboard but I have upgraded to a Quad since then. Hope my new 3570K is still going strong 6 years from now.