If your board says it will support the 1055 then it will, but without 8+2 phase power you really shouldn't be looking for 4ghz overclocks. I think I personally would quit around 3.4-3.5ghz range. Even the 890FX boards that only have 4+1 phase power have had exploding issues from time to time with significant overclocking done on them. Think about selling your board on craigslist and buying a used 790x-ud4p here on the marketplace. I believe there is one up there, if I'm remembering right it's even one of the posters in this thread selling it.
As for the cooler, I am currently running 1.475v at 4GHz, and am peaking out around 44-45C while being completely silent, your 40-41C for 3.1GHz really isn't 'great', I have trouble believing it could get any proc up to 4GHz. I could be wrong though, because I really don't know much about the GeminII S. BlackOmega linked a very high end cooler on the other page, you don't need something THAT high end to get an AMD chip to 4ghz, you'd most likely be fine with nothing more then a Scyth Mugen 2.
You'd be best off with a 955 if you still have to buy, if your family bought you the 1055 already then grats, you just got a great processor and it'll do you great in the 3.4-3.5 range.
You also asked about max temps, you want to peak some where in the 62+C range, the temp sensor reads on average about 10C low, so you don't want to be going a whole lot higher then 52+C when in Core Temp. So when I'm reading 44C while stressing I'm actually more likely around 54C. You get the idea.
Edit: ^ Temperature information was meant for the 1055 only!Edited by Pao - 12/22/10 at 11:23am