I tried posting this question from my iphone.  Doesn't appear it worked.  If I'm repeating myself I apologize.  

My chiapetta/cosenza has 3 or 4 dozen figs on it.  They haven't ripened yet and I'm running out of time.  Lately they appear to start to change color like they are going to ripen - but then they just fall off.  The plant looks healthy and so does the fruit.  What causes this?  Would more heat help them?  I've kept them out of the greenhouse because I was told that can compromise the flavor.  But at this rate I'll take what I can get.  Any advice is appreciated.  Thanks

Hi ajv73,
Call it the learning curve .
When a fig tree drops the figs, this is due to a problem in the conditions of the tree,
excess or lack of :
Water
Sun
Fertilizer
heat
So a lot to choose from. Because we're heading to Fall season, I would blame it on temps - but could be any of the other problems.
I myself bought a "Pastiliere" and it dropped 3 of 6 figs - yes that makes me sick BUT this is part of the normal learning curve. When you try a new strain,
you will meet those pitfalls and disillusions !
I had been shying away from "Pastiliere" and "Ronde de bordeaux" because nurseries have been pushing them ... But I don't see people screaming hourras about those fig trees ...

But, ok, patience is a virtue, and one has to have a lot of virtue to grow fig tees in my Zone7 and you're in Zone6 !

I'm still waiting on the main crop of my bigger fig trees ( ufti and Goutte d'or), and with the mild freshy weather that we have here since the first week of August (really unusual)... Well that stinks !
So try in the future to target brebas crops ( like I do ) - Just saying, you're free to do what you want :) .

No way of knowing the problem for sure. But I'm guessing it's heat too. In order to give it a chance I put it in the greenhouse. It's getting big so that was a bit of a chore. We'll see what happens.

What type of figs with good breba crops do you recommend? Thanks

I find figs in containers sometimes drop some figs probably for the reasons jdsfrance gave.  I think water is the biggest factor.  If I forget to water them for a few days after the figs are well formed then some figs will get wrinkly and drop.
We had a few weeks of nice summer weather but now they are saying 15C highs for the next week so I moved my containers into the greenhouse until it warms up again.