Ambient temps affect idle temps far more than load temps. You gotta figure the heatsink and any air blown across it are starting out at whatever the room temp is. Load temps will go up from there, but it depends a lot on the load and the efficiency of the cooler as to how high they can reach. So in summer, you can expect idle temps of ambient + @10°C ±, so maybe high 30's to very low 40's. That's not all that bad. Loads change things, so does efficiency, so you may just as well end up stress testing and getting 84°C, which puts gaming @70% of that or high 50's-60ish°C.
Or with a lower efficiency cooler it might climb into the low 90's or high 60's-70ish°C gaming.
The cpu can live with those temps just fine, if you can then no, you don't need a better cooler, but it sure wouldn't hurt.
Your location and availability and case and budget and OC is going to determine any recommendation, but generally expect that bigger is always better.