According to [this source](http://www.chabad.org/therebbe/article_cdo/aid/148182/jewish/Who-Will-Build-the-Third-Bais-Hamikdash-Man-or-G-d.htm), it may be a moot point. While Rambam claims that the Third Temple will be built by Moshiach, Rashi states that Hashem has already built the Temple in the heavenly realm and it will descend to earth upon arrival of Messiah. I recall hearing somewhere that the Temple will be made of some form of impermeable metal, suggesting it will be an everlasting structure. 

If Rambam is correct, I am willing to guess that with instructions given to Messiah by Hashem, available technology (based on the instructions, aka, blueprint) will be used just as it was true for the first two temples (tools such as hammers, hoists, chisels, etc. was technology of the day back then.)