For a pre-built, the g3-710 has potential. You really don't need a new case unless you want one and interior aesthetics really don't play into the solid sided case, that's more window dressing. As is, it's a pre-built, so most of the connections to the front panel are almost always proprietary, which can make swapping to an aftermarket case a nightmare to either get adapters or run pinouts to figure out which is the power, power led, hdd led etc. Usually more trouble than it's worth.
Without running the serial numbers or model number of the psu through Google, it's generally impossible to actually state the psu quality on a designed gaming pc, it's entirely possible it's a Delta OEM unit or Seasonic OEM unit, which puts it as a very good unit, definitely better than almost all the low budget aftermarket psus. Being @500-550w to be paired with a gtx970 narrows this a little since most of the real junk is usually in the 300w and lower class.
As is, I'd start with 2x things. First figure out what can and cannot be done with case cooling. Ideally you'll have 2x input fans and 2x exhaust fans, but that doesn't look feasible with your case.
You actually have no pre-installed case fans, totally relying on the top mounted psu fan for exhaust, which is where your temps are coming from. I'd give serious consideration to using the hot-swap bay for your hdd, and removing the lower hdd bracket and getting some fan mounted in the front. I'd also figure out exactly what size fan will mount below the psu and get one mounted there. A budget cpu cooler, like a Cryorig H7, paired with a rear exhaust fan would do wonders there for all temps as now most heat will be directed out the rear end.
8Gb ram is fine. Gtx970 is fine. 128Gb ssd is fine just takes a little space management and keep games on the hdd. For a medium range build, it's really not that bad. Just airflow is a consideration.
The only other thing I'd swap would be the cpu. The i5-6400 is a dog. It's quite easily beaten by the i3-6100 in most of your everyday games, especially online games like cs:go or LoL.
http://www.hardwarecanucks.com/forum/hardware-canucks-reviews/71760-intel-skylake-i5-6500-i5-6400-i3-6100-review.html
I'd give real consideration to an upgrade, it's more than possible to get a used i5-6500 or better yet a I7-6700, both of which will require nothing more than a bios upgrade, as the G3 comes available with that cpu. You might even go so far as contact Acer directly and find out if the kabylake cpus will be upgradable, if bios supports it, an I7-7700 would be the ultimate goal. Definitely add a Cryorig H7 and at least a rear exhaust fan for any i7 move.
Just my thoughts.