The Meenakshi temple did not exist in sangam period. It is later construction only. As of now, the EARLIEST temple we have is the Mandakappattu kudaivarai ( between villupuram and chenji ) built by Mahandra varman during 6th century. See more details about that temple in the 7th issue of Dr.Kalaikkovan's Varalaaru magazine.
I've read in 'Madurai Through The Ages' that the Meenakshi Temple existed in the post-Sangam period (3rd century AD onwards) - of course, it was much smaller then.
In most cases, we find that outermost shell of the core sanctum sanctorum alone existed in olden days. I am not sure about Madurai, but I know very well about Srirangam and Thirumala temples - both of which are referenced in Silappadhikaram.
Pallavas constructed their own temples - they did not touch the currently existing temples. INTERESTINGLY, NAYANMARS AND ALWARS WHO ALSO BELONGED TO THIS PERIOD DID NOT SING ONE COUPLET ON THESE NEW TEMPLES. They continued to sing only the old temples which were already in existance. Thus it is wrong to surmise that it was mahendra who built the temple. Thirunavukkarasar lived during the period of mahendra and walked all over tamilnadu singing hundreds of temples.
Early pandiyas, adigamans and other chieftians followed this early trend. Kalugumalai vettuvan koil, namakkal kudaivarais, naarthamalai, kodumbaloor moovar koil....etc
Cholas did very useful contributions to all old temples - like renovating them as katralis, adding maha mandapas, prakaras etc. MOST OF THEIR WORK REVOLVED AROUND OLD TEMPLES, THOUGH THEY ALSO CONSTRUCTED LOT OF NEW TEMPLES. Aditya reconstructed 63 (or 64) such temples along banks of cauvery. Rajamahendra did renovations to srirangam temple sanctorum where water was seeping thro the floors. He also built the second prakara called even now by his name - raja mahendran thiruveedhi. Most of their work was done in chola mandalam and slighty lesser work in thondai mandalam and pandi mandalam.
Then came pandiyas... once again worked along the line of cholas. Did most contributions in pandi mandalam and chola mandalam.
Then came vijayanagar rulers / nayaks. They took the loafty responsibility of brining all temples ruined under islamic rule back to worship. They infact collected fragments of highly dilapated temples and assembled them in temples that retained better shape. The contribution of kambana udaiyar & nayak successors cannot be forgotton in tamil history. But for them we would have lost most of our ancient treasures.
Incidentally it was devi madurai meenakshi who inspired kampana udaiyar in his dream to wage a war against islamic rulers and ordered to restore the hindu temples back to their form. That is another story altogether....