If you want to reach 4ghz for your target overclock you are better off going with an am3 board rather than am2+. I suggest a 790 chipset and full dd3 ram. I have the x4 955 currently and I hit 3.8ghz on it with the ma790fxt-ud5p mobo from gigabyte. I am using OCZ Reaper 1600 mhz memory and have no stability issues at all unless I start creeping up towards 4ghz. You also want to make sure you get the latest c3 125w 965 or else you are just getting a 955 with increased voltage.
You say to leave the cooling aside, that is foolish because without a decent cooler you will get no where close to what you want without being extremely hot.
I have the ssme procy on a Am3 board (MSI 790FX-GD70). You might wanna know that I have OC'ed my processor to 3.8Ghz @ 1.475V and it runs very stably with temps never reaching the 50s (AMD 965BE have a threshold temp of 62-65). However, increasing it even 1 Mhz over 3.8 crashes it instantly. I use the Corsair H50 in an Antec 1200 for cooling.
Other people have also had similar problems with this processor. Its not very stable beyong 3.8Ghz.