When are we talking? The functions and duties of the aediles changed quite drastically over time. Originally they were basically baby tribunes, overseeing the plebeian temples, but when the office was expanded to include patricians their powers were vastly increased. Throughout the history of the magistracy the aediles held kind of funky and seemingly random duties, although in the end we could group all of them into the general category of "public oversight," the protection of the public in a less direct way than the immediate political championing of the tribunes. During the late Republic the office enjoyed really quite shocking power--Caesar's aedileship is the most famous of the period, but probably the least important. Cicero as curule aedile threatened to prosecute Verres under the auspices of provacatio, the legal appeal to the people against injustice by a magistrate (the idea, presumably, is that as an overseer of the public the aedile had the right to represent them in such a case--whether this is so or not is unclear, as Cicero only claims that he can do it and gives no details), and Clodius as aedile accused Milo of violent action. But soon after, under Caesar and especially under Augustus, the office of the aedile lost a great deal of power, so it's important to know precisely when we're talking.

During the Republic the main functions of both the curule aediles and the plebeian aediles were pretty much the same. Cicero lists the aediles' duties as being care of the grain and general food supply, oversight of certain public games (the plebeian aediles traditionally oversaw the plebeian games and the curule aediles oversaw pretty much all the other games), and the oversight of the city. Oversight of the city (cura urbis) is a bit vague, but it consisted of making sure the city was in good order, caring for streets, sewers, the organization of the forum, the maintenance of proper cult practices, and stuff like that. It also included the right to prosecute on behalf of the people against extortion, rape, and various crimes like that. They appear to have overseen all buildings in the city by the late Republic, making sure they were legal and stuff, and they could exact fines for breaking the law. Originally, however, the aediles did not have this power. Before the introduction of the curule aediles the aediles oversaw only the plebeian temples on the Aventine (those of Diana and Ceres), as well as serving as deputies to the tribunes (a function they lost soon after--the OCD says they outranked tribunes by Cicero's time). Augustus stripped them of a number of their powers, especially their abilities to prosecute and so forth, but also their ability to oversee what games were still allowed to them (which was given to the praetors). Under Caesar they had already lost their rights to oversee the grain supply, which was given to the newly-created aediles Ceriales, which Augustus then dissolved and turned into a larger magistracy. I don't know of any information for the loss of their oversight over all the buildings in the city once they had gained it sometime in the Republic, but their powers must have been divided, since during the Principate we know of separate minor magistrates that inspected the aqueducts and the granting of private use of the water supply was the right of the emperor, whereas previously the aediles had had power over the aqueducts.

So the short version? It depended. In any case, even after the aediles had oversight over the whole infrastructure of the city they still focused most on the temples. Maintenance of the temples probably did not, however, mean keeping them in working order, as if they were some sort of machine, or renovated or anything like that. It consisted of overseeing cult functions, priestly duties, and votive offerings.