Yes the 965 has a slightly better HSF than the 920/940 however, it still is only adequate for average usage that is not 100% system intensive. If you research Intels designation for the 130TDP they do not set that as the "total" output like the name implies, it is an averaging that nominal use should fall within. Stock i7s can output close to 200 watts of heat and it climbs with an overclock.
The copper would obviously help but in all honesty, ripping off the fan and putting a high CFM fan on it would help more. A quality aftermarket HSF would be an improvement over that obviously.
If you are not doing any overclocking and don't run extremely intensive graphical rendering or video/audio encoding/decoding that uses multithreaded applications, then it would work ok I suppose. I personally wouldn't recommend it though. $1000 cpu in a multi-thousand dollar machine, I would spend damn good money on a suitable cooling system and a rock solid dependable power supply. Inadequacies in either component can cost you your CPU, you have to judge what that's worth to you.
All said though, even burning up an i7 is actually pretty hard. They downclock @ 98C and shutdown at 102 or 105 automatically to prevent destruction that way. Make sure you DO NOT turn off your heat and voltage shutdown limits in your bios if you run the stock HSF, and obviously, forgo any overclocking unless you are willing to buy another cpu right now.
I recall an old saying,"No matter how much you polish a turd, it's still just a turd." The stock Intel HSF is a turd, the 965 happens to be a 50% copper turd. Just my 2c