In reply to Lieven De Vlaminck:
June will be fairly cool. However to some extent it depends on what you are going to do.
The Garganta camp on Huascaran is at 6000m and is a seriously cold place. On the other hand the camp on Tocllaraju is at c5000m and less of an issue. The valley base camps at c4000m are usually relatively mild.
The combination of a 600 bag and a good quality liner, say +5, is certainly the most flexible option but if you really feel the cold and you want to go as high as possible then I think that an 800 bag is the best bet.
I use either my 600 or my 800 bag depending on the trip. Having both is an expensive option but if you want to do a lot of high altitude and alpine climbing then IMO it is essential to have both weights of bag. For a one-off the 600 bag and the liner make better sense.
You also need good ground insulation. For 5000 to 6000m camps I use a full length Z-Lite pad with a short Thermarest pad on top. A cheaper alternative for a one-off trip is to use a 4/5mm carpet underlay pad beneath the Thermarest. You can buy the underlay in Huaraz.
Regards and Good Luck, Cliff.