Just another 2 cents from me: I haven't been to Iraq, but if the heat is anywhere near as oppressing as it was in western Afghanistan (I actually saw the thermometer hit 145F...and we still ran missions ... avoid the summer months like the plague.
And another thought: You are aware that Operation Iraqi Freedom is now known as Operation New Dawn? There are very very few infantry / combat units left in Iraq right now, everything is pretty much done by the Iraqi army. Guys deploying to Iraq are no longer getting combat patches because the major combat is over. Although tribal / religious violence is still prevalent, even sometimes in the Green Zone in Baghdad. I wouldn't recommend traveling there at all.
There is always the option of traveling to a place where a previous war was. I spent 2 weeks in Sarajevo, Bosnia not too long ago. That city hasn't really been rebuilt after the war there. Damn near more bullet holes in buildings there than I saw in Farah. Sort of cover the fall out and after effects of a war zone. Or what about a trip to the cities around Chernobyl? There is plenty of messed up stuff to see there.
Off topic: My buddy Hakan is a Swedish Major, didn't the Swedish army just stop conscripts?