As Stephen Oakley (referenced below, at p. 342) observed:

1. “This was probably Rome’s first temple to Venus.”
   

It seems that it was built on the Aventine and dedicated on the feast of the Vinalia Rustica (an annual festival held on 19th August) since

1. ✴Varro recorded that:
   

2. “The 19th of August was called the Vinalia Rustica because, at that time, a temple was dedicated to Venus and gardens were set apart for her, and then the holitores (kitchen gardeners) went on holiday”, (‘On the Latin Language’, 6: 20,  translated by Roland Kent, referenced below, at p. 193)
   

3. ✴the entry for this date in the fasti Vallenses records:
   

4. “VINALIA; Veneri ad Circum Maximum”, (see, for example, Howard Scullard, referenced below, at p. 177).
   

The epithet ‘Obsequens’ indicates that, in this form, Venus was ‘favourable, indulgent, gracious, propitious’ (see the ‘Latin Dictionary’ of C. T.  Lewis and C. Short).  Its first appearance in our surviving sources is late: it is taken from a passage by Servius (4th century AD, in his commentary on Virgil’s ‘Aeneid’:

1. “dicitur etiam Obsequens Venus, quam Fabius Gurges post peractum bellum Samniticum ideo hoc nomine consecrauit, quod sibi fuerit obsecuta.  hanc Itali †Postvotam† dicunt”, (’ad Aen’, 1: 720).
   

2. We still call Venus ‘Obsequens’: this is the name of the goddess that Fabius Gurges consecrated after having completed the war against the Samnites, because she had been propitious towards him.  The Italians call it postvota [which seems to indicate a vow that was conditional on a satisfactory outcome] (my translation and explanation of postvota).
   

Chronology According to Servius

Stephen Oakley (referenced below, at pp. 342-3) observed that Servius’ phrase ‘after having completed the war against the Samnites’ here:

1. “... suggests (although it does not actually state) that Fabius Gurges vowed the temple either as consul in 292 or as proconsul in 291 BC ... to encourage Venus to help him [complete the Roman victory over the Samnites].”
   

The context in this case would have been provided by:

1. ✴Livy’s record that:
   

2. “... Gurges defeated the Samnites [as consul in 292 BC) and celebrated a triumph [in which] Pontius, the Samnite commander, walked in the [triumphal] procession and was [then] beheaded”, (‘Periochae’, 11: 1).
   

3. ✴The record in the   ‘fasti Triumphales’ of Gurges’ triumph over the Samnites as proconsul in 291 BC. 
   

Chronology According to Livy

Livy himself described the decision to build this temple after his account of the major victory that Gurges’ father, Q. Fabius Maximus] Rullianus, had secured over the Samnites, Gauls and Etruscans at the battle of Sentinum in 295 BC:

1. “As far as military operations went, the year was a prosperous one, but it was rendered an anxious one by a severe pestilence and by alarming portents.  In many places, showers of earth were reported to have fallen, and a large number of men in the army under Appius Claudius were said to have been struck by lightning.  The [Sibylline] Books were consulted in view of these occurrences”, (‘History of Rome’, 10: 31: 8).
   

He then recorded that:

1. “During this year Q. Fabius [Maximus] Gurges, the consul's son, who was [presumably a curule] aedile, brought some matrons to trial before the people on the charge of adultery.  He obtained sufficient money out of their fines to build the temple of Venus that stands near the Circus [Maximus]”, (‘History of Rome’, 10: 31: 9).
   

In this scenario, the building of the temple would have been the result of the consultation of the Sibylline Books.

Probable Chronology

Stephen Oakley (referenced below, at p. 343) argued that: 

1. “Livy’s account of the origin of the temple [in a decision taken in 295 BC] is much to be preferred [to that of Servius] because:
   

2. ✴it is anchored in a secure and plausible chronological context; and
   

3. ✴when [matrons] had been convicted of [adultery], the prosecuting aedile ... may well have thought that the goddess of love and sex needed appeasing.  If the building of the temple was started by Gurges [in 295 BC, as recorded by Livy] but the dedication took place only in 292 or 291 BC, then this  may explain why Servius associated it with the fighting of those years.”
   

It seems to me that this chronology is probably correct, but that there might well have been other reasons for Gurges’ choice of Venus Obsequens (conveniently in accordance with the advice of the Sibyls):

1. ✴the Samnites had probably violated the Aphrodision near Ardea after their victory at Lautulae in 315 BC (above);
   

2. ✴Gurges father, Q. Fabius Maximus Rullianus had just secured major victory over the Samnites and their allies at Sentinum, but that the war in Samnium continued; and
   

3. ✴Gurges might well have judged that this would be exactly the right moment to:
   

4. •solicit the help of Venus in defeating and punishing the sacrilegious Samnites; and
   

5. •advertise his own intention:
   

6. •to stand for the consulship in the near future; and
   

7. •(hopefully) to complete the task that his father had begun.