There are always two sides to a story. You should stick to the terms of the contact, which means honoring the fixed price assuming the scope was delivered, no matter if late (claiming any penalties if you had them in the contract). However, this also means to pay attention to the oft times ignored assumptions, exclusions, limitations, and any other exceptions written in and agreed to within the contract.
Complaining that they worked more than expected is a weak argument and a non starter. Unless they're completely unsophisticated and way outside their depth, my bet is they have a laundry list of items that meet to some degree the exceptions written into the contract and that you grabbed the weakest of the arguments in your OP. I don't know you but I watch this all the time. It's a form of confirmation bias so you sort of paint a picture to get the results you want to hear. YMMV.
That said, sit down and have a professional, open conversation and listen to their arguments and look at the contract and see how they may fit in the terms and conditions to which you agreed. A win-win outcome is best for all of you, protecting both of your interests and your long term relationship. If they truly have nothing to stand on, then commit to helping them with a better contract next time so you two can be true partners in it for the long term. If they're facing extinction, and you value them and their work, you may want to consider violating your agreement and get them in a better place if you can afford to do so. Long term wins.
