This may be normal for the stock cooler. I have been experimenting with a E4300 on a gigabyte p965-ds3 board(no overclocking). Measuring with intel thermal analysis tool(TAT) It shows the two cores at 52c-54c at idle. Speedfan shows the same for core0 and core1. Speedfan shows temp1=40c, and temp2=38c, which I assume is some case temperature. The ambient temperature is 29c. The case is very well ventilated and the heat sink fan is operating.
With TAT stressing the cpu, the core1 & core0 rise to 67c. It seems stable. I removed the stock heat sink, and checked both the cpu and heat sink for flatness, and they seemed to be ok. Initially, I may have had too much as5, and I tried using very little, but this gave no real change. I am now running with as5 using the recommended application method. I have some shin-etsu x23 on order, and I will see how that works. At this point, I think that either the stock cooler is not as effective as I had first thought, or there is some issue of quality control between the cpu chip and the heat spreader.
I am not overly worried because this is a test machine, and the cpu is supposed to throttle back or shut down if it gets too hot.