34 C is a very hot room--about 93 Fahrenheit. Most people's rooms are probably 22-24 C, or somewhere in the 70s Fahrenheit.
You can't expect to have a cool CPU with high ambient temperatures like that unless you have a very powerful fan with good case ventilation. Even then, I wouldn't expect a lot of improvement. It's very tough fighting high ambient temps.
I wouldn't consider a new heatsink until I knew that my case had good case fans to begin with. If you have poor case ventilation in a very hot room, you are fighting a losing battle.
Are these idle temperatures or load temperatures?