This event is depicted in Chapter 55 of Livy's History of Rome. Essentially, King Tarquinius was keen to leave a spectacular monument that would illustrate his power and wealth. However, Livy uses his account to ingratiate himself with Augustus and the administration, by discussing the omens that presented themselves during the construction of the temple. Now, I'll leave Livy to provide a full description. Thanks for the translation go to my Latin teacher, Bill Huntingdon. Any Classics scholars will notice it's fairly literal, hence the convoluted nature of some of the sentences.

When Gabii had been taken, Tarquin made peace with the Aequians and renewed his treaty with the Etruscans. Then he turned his attention to affairs of the city. The first of these was that he should leave the Temple of Jupiter on the Tarpeian rock as a monument of his reign and his name: of the two Tarquin kings, the father had made the vow and the son had fulfilled it. And so that the whole area of Jupiter and of his temple which was being built should be free from other religions he decided to deconsecrate the shrines and chapels, several of which had been vowed, consecrated and afterwards inaugurated there by King Tatius first at the very critical moment in the battle against Romulus. It is said that at the beginning of [the building of] this work the Gods gave a sign to indicate the power of so great a dominion. For though the birds were allowing the deconsecration of the chapels, in the case of the Shrine of Terminus they did not give assent; and that omen and augury was taken as follows: namely the fact that the seat of Terminus had not been moved and he alone of the Gods had not been called forth from the place consecrated to him meant that everything would be strong and stable. After this omen of perpetuity had been received, there followed another portent signalling the greatness of the dominion: a human head with its face intact is said to have appeared to those opening up the foundations of the temple. When this sight was seen it meant unambiguously that it would be the citadel of the dominion and the capital of the world; and the soothsayers told of this thus, both those who were in the city and those whom they had summoned from Etruria to consider that matter.

The king inclination’s towards expense was increasing; and so the prize money from Pometia, which had been destined to take the work up to the gable, scarcely sufficed for the foundations. For this reason, I would rather believe Fabius, besides the fact that he is older, that there was only forty talents [taken from Pometia], than Piso who writes that forty thousands pounds of silver by weight were set aside for that task, a sum of money not to be expected from the spoil of a single city then, and likely to exceed the costs of any building, even in modern times.