Should the United States work together with Iran to defeat ISIS/ISIL?

Link: Cooperation between the U.S. and Iran?

Are we prepared for the possibility of cooperation between the United States and the Islamic Republic of Iran?  On Friday, a plane carrying U.S. contractors on their way from Afghanistan to Dubai was forced to land in Bandar Abbas, Iran.  It would have been no surprise if the Iranian authorities had caused headaches for the United States by keeping the plane grounded.  But for some reason, the issue was resolved quickly and the contractors made it to Dubai in time for the weekend Camel Races.  Personally, I would have expected the Iranians to create some international incident, and the fact that they didn't could be a message that the Iranians are open to some sort of dialogue.  Its possible that Iran views the threat of ISIS/ISIL as more of a danger than American Imperialism (at least temporarily).  What would lead Iran to consider working with the United States against ISIS/ISIL, and what could be gained by such a rapprochement?

Iran is an Islamic Republic, but it is a Shia-only club.  Iraq was traditionally governed by Sunni Muslims, which fueled the animosity that lead to the 1980-88 Iran-Iraq War.  ISIS/ISIL is a Sunni-based terrorist movement, and has shown a willingness to attack Iraqi Shia targets.  In fact, Iran has sent military support personnel to assist the Shia militias that ostensibly are in place to protect Shia holy sites in Iraq.  At this stage Iran must recognize ISIS/ISIL as its most dangerous external threat.  ISIS/ISIL has grown in both manpower and firepower as it continues to reap the harvest of new recruits and abandoned Iraqi and Syrian military equipment.  For all of its support for terrorist groups like Hezbollah, Iran is basically a functioning republic with a regular army.  ISIS/ISIL, with its unpredictable nature and its ability to change strategy quickly, is just the kind of foe the Iranians want to avoid.  One would assume that Kurdistan would be the direction from which ISIS would invade Iran, which would mean that ISIS/ISIL would have to defeat the Kurdish Army and the Pesh Merga (Kurdish paramilitary) first.  But ISIS/ISIL has shown tremendous quickness of movement and unpredictability, and might just pop up somewhere else on the Iraq/Iran border.  The Iranians are correct to consider ISIS/ISIL a real threat to their national security.

Would a joint anti-ISIS/ISIL effort on behalf of Iran and the United States be successful, and is it a possibility to begin with?  Both Iran and the United States have the military means to destroy ISIS.  But it is doubtful at this stage that either has the conviction.  The United States has the means to render ISIS/ISIL ineffectual (at least temporarily) from a prolonged air campaign alone.  The Iranians, with an inferior and aged Air Force, would be obliged to use large numbers of troops (and to cross the Iraqi border).  But ISIS/ISIL is hindered by its present lack of cohesion.  Is it a terrorist organization or an army?  Have enough volunteers swelled the ranks that supply has become a daily concern?  Has ISIS/ISIL captured so much equipment that it has become a burden to what was once a lean, stealth-like organization?  ISIS/ISIL is vulnerable, especially from a supply perspective.  But again, the issue for both the Americans and the Iranians is conviction.  Does either side want to make the call to devote the resources necessary to send ISIS/ISIL back to the Stone Age?  As of right now, the answer is no.

For anyone who seriously hopes for peace in this region, any cooperation between Iran and the United States must be seen as a positive development.  But I just don't see it happening.  And the problem isn't in Washington DC, its in Teheran (or should we say Qom).  The religious leaders of the Islamic Republic will never be able to reconcile themselves to cooperation with "The Great Satan".  The United States has extended the Olive Branch on more than one occasion in the last decade, only to be meet with a cold shoulder.  The non-interference with a planeload of U.S. contractors on the tarmac of an Iranian Airport is a very surprising and encouraging sign.  But this relationship will improve with tiny steps (such as the one just mentioned) over an extended period of time.  But the situation could become fluid quickly.  The Iranians want to do whatever they can to keep the U.S. Army from returning to Iraq. Maybe some sort of joint military operation (as unlikely as it is) that eliminates ISIS/ISIL, would be the one development that keeps large numbers of U.S. troops from returning to Iraq.

(This is a very interesting question and I very much welcome all other considerations and opinions.  Please comment!)