Yeah it wasn't fun.
The back corner of my case was near on impossible to touch after a short while.
There was one game which always brought it to 110degC.
The cartoon Star Wars Knights of the republic at max settings
The graphics were basic but it stressed my card none the less.
My solution was to upgrade the cooler, edit and flash the GPU BIOS so the twin turbo fans would start at 60% fan speed.
Otherwise they would not kick on at all without software.
The card you have is non reference PCB.
Gigabyte may have done a nice job on the power phase revision of the card over the reference which kept the VRMs cool enough not to need a VRM cooler.
In my case the memchips were indeed crap.
One name synonymous with poo chips......Quimonda.
When I removed the stock cooler and saw them i knew there was a likely hood of getting a poor mem OC.
Even so there are people who have apparently ran stable at 1100Mhz with the card I have.
I increased the voltage on mine at one stage and it did squat.
Still artifacts.
Oh well at least I don't fidgit around in my seat due to the heat my card was dishing out.
I would expect the heatsink to get hot but that is showing there is heat being transferred and dispersed which is much better than none in your case.
My stock cooler had warning stickers and one of them was right next to the VRM cooler.
I would look for a decent heatsink and use sekisui thermal tape to attach it to the VRMs.
An accelero S1 and add a fan to it or a twin turbo would be your best bet but I don't think Arctic Cooling makes the standard Twin Turbo anymore.
Only the Twin Turbo Pro with 92mm fans.
You will also find with the Twin Turbo Pro, the copper pipes run slightly above a couple of VRAM chips which leaves no space for adding even low profile cooling modules to.
You will most likely have to edit the GPU BIOS as well to get the fans to run if you do not want to rely on software for your fans to run.