Unfortunately, the DG965WH does not support any of the 45nm processors at all. Nor does it support FSB speeds above 533MHz (FSB1066).
BIOS download for Intel Desktop Board DG965WH
The latest BIOS version available is listed as 1754.
Compatible Processors for Board DG965WH
Lists many processors, like, for example, E6700 2.66Ghz Core 2 Duo. On that same page "Min BIOS Version" is 0816.
It seems like the processor compatibility tool has some problems. Looking at my BIOS setup screens it looks like the DG965WH FSB is 800MHz, and many of the upgrade processors in the grid are at 1066MHz or better. Can the board actually run at 1066MHz? Where do I download the BIOS upgrade version 0816?
See http://communities.intel.com/message/141554#141554 for the answer to my own question. BIOS 0816 is very old - original as released when the board was first developed. The BIOS versioning has incremented from 1400's to 1600's and now most current is 1754. The processor compatibility matrix apparently defaults to the original BIOS for minimum functionality.