From your explanation, it's very clear that your heatsink is not secured properly to the cpu back. On stock heatsink/fan solutions typically it comes with pushpins that locks on the motherboard (actually there is a small how to connect heatsink manual if I remember correctly) while turning those locks. There is a good possibility, that It might seem to you that it's secured but most probably it's not. Thus when you have your case up the heatsink/fan weight is lifting it from the surface, while you place your chasis horizontal it rests on the cpu back because of it's own weight. (I'm guessing here that you have applied thin film of paste on cpu back to increase the transfer of heat from cpu to heatsink - bear in mind don't put a lot of paste since it may run off the sides and may spread on motherboard causing improper contacts)
If you determined after the inspection that the heatsink/fan assembly is locked properly on your mobo then you have few options as below:
1. Buy an aftermarket heatsink (non-Intel) and install.
2. Get a new stock heatsink/fan - you might have damaged springs/pushpins of the exisiting stock heatsink
3. Get an exact hole size (as of mobo) plastic/pvc spacer of 1mm/2mm thickness and place behind the mobo, push the pushpins on heatsink/fan assembly so that it locked and is secured even if you turn the mobo upside down. The idea is to get rid of that extraspace and secure the heatsink/fan assembly on mobo.
Hope this works!
I have the same CPU and was running hot, but only got real bad when I ran games. The system would shutdown for overheating (hit about 85C before it shutdown). I bought a coolermaster hyper N520 and now I'm gaming at 44C and resting at 30C. I recommend you do the same. The coolermaster fan is much easier to install than the stock intel fan and screws in securely.