The Temple of Jupiter Stator was a sanctuary on the slope of the Capitoline Hill. In Roman legend, it was founded by King Romulus after he pledged to build it during a battle between the Roman army and that of the Sabines.
The Battle of the Lacus Curtius took place in the Forum area between Romulus and Tatius, king of the Sabines. The Romans had been forced to retreat uphill on the Via Sacra. However, at the Porta Mugonia, Romulus prayed to Jupiter and vowed him a temple if he stemmed the Sabine advance. The Romans regrouped and to held their ground, staving off defeat.
On that spot, Romulus founded the temple, probably near or just outside the Porta. The sanctuary was most likely not an aedes but only an altar, enclosed by a low wall or fence.
In 294 BC, Marcus Atilius Regulus made a similar vow in a similar situation, when the Romans were losing a battle against the Samnites, but they miraculously turned around, regrouped and held their ground against the enemy.
On November 8, 63 BC, it was in the temple that the senate convened to hear the consul Marcus Tullius Cicero deliver his famous first of the Catiline Orations, against Catiline.
The temple was destroyed in the Great Fire of Rome during Nero's reign in July of the year 64.
Since the Porta's site is not known, the temple's location is not known with absolute certainty. The written sources give some hints, such as near or just outside the Porta, on the higher end of the Via Sacra, or just on the Palatine Hill, the site of Romulus's Rome.
Livy states that the temple was located near the royal palace at the time of the death of Lucius Tarquinius Priscus, near the "new street" (nova via) and that Queen Tanaquil addressed the people from the palace window.
There is a fair amount of consensus on a location just besides the Arch of Titus on the northern slope of the Palatine Hill. When a medieval tower was demolished in 1827, the ruins of an ancient building appeared, and the remains are frequently identified as the foundations of the temple.
The Italian archaeologist Filippo Coarelli places it closer to the forum, between the Temple of Antoninus and Faustina and the Basilica of Maxentius, where the Temple of Romulus stands. His line of reasoning is based on the course of the Via Sacra before the construction of the Basilica of Maxentius, the known borders of the ancient administrative regions of the city and the literary sources listing the monuments in each region. The location near the Arch of Titus does not fit since it is in the wrong administrative region and not in the right position relative to the other buildings listed by ancient writers, but the Temple of Romulus on the Via Sacra is a perfect match.