I can't find any information about who the temple could have honored. There is a large Roman temple partially reconstructed next to City Hall, but it's not near the mosque and no one seems to know whom it was dedicated to.
I found a map of the Roman city. The Roman bridge, which is still in use, leads to an old archway to enter the city close to the mosque/cathedral, and it seems to have a relief of Venus as the protectress of the city. The bridge and archway are connected to the city's main road, which passed through what is now the mosque and the heart of the old city. The site of the original, somewhat small Visigoth church is located alongside that road.
The Visigoths probably didn't profane the site, though. The Vandals came through first. I don't know what they did to Cordoba, but they leveled Seville. (Julius Cesar was an important mayor of Seville, by the way.) I imagine they did harm to Cordoba, too. The Vandals are the reason there are few Roman ruins in Seville, and there are few in Cordoba, as well. Then the Vandals left, and good riddance.
In contrast, the Visigoths, who came afterward, stayed and tried to govern, but they were so incompetent that when the Muslim Moors took over, they got a fairly warm welcome from the local populace in many place. The Moors were orderly and peaceful, and Visigoth war-ridden chaos had been unpleasant. The Visigoths actually converted from Arianism to Roman Catholicism in an attempt to make the locals accept them better, but that didn't smooth out all the problems.
Re: I wonder who the original Roman temple honored?
I found a map of the Roman city. The Roman bridge, which is still in use, leads to an old archway to enter the city close to the mosque/cathedral, and it seems to have a relief of Venus as the protectress of the city. The bridge and archway are connected to the city's main road, which passed through what is now the mosque and the heart of the old city. The site of the original, somewhat small Visigoth church is located alongside that road.
The Visigoths probably didn't profane the site, though. The Vandals came through first. I don't know what they did to Cordoba, but they leveled Seville. (Julius Cesar was an important mayor of Seville, by the way.) I imagine they did harm to Cordoba, too. The Vandals are the reason there are few Roman ruins in Seville, and there are few in Cordoba, as well. Then the Vandals left, and good riddance.
In contrast, the Visigoths, who came afterward, stayed and tried to govern, but they were so incompetent that when the Muslim Moors took over, they got a fairly warm welcome from the local populace in many place. The Moors were orderly and peaceful, and Visigoth war-ridden chaos had been unpleasant. The Visigoths actually converted from Arianism to Roman Catholicism in an attempt to make the locals accept them better, but that didn't smooth out all the problems.
http://www.cordoba24.info/english/html/temploromano.html
http://www.artencordoba.co.uk/ROMAN-CORDOBA/Roman-Cordoba-Monuments.html
http://www.artencordoba.co.uk/ROMAN-CORDOBA/img/PLANS/PLAN_CORDOBA_COLOGNE_PATRICIA.jpg