Since everything is computerized now, when the Bais HaMikdash is rebuilt, will we use the computer to rebuild? I.E., the measurements for the offerings, the entire rebuilding, etc.?
The Temple Institute (מכון המקדש) is a Jerusalem-based organization whose goal is to build the Third Temple. As such, they have invested serious money into planning. (A visit to the visitor's center is well worth it, from experience. And it got even better since i was there a few years ago.) They already have the kohanim's clothes, k'toret (incense), and most of the keilim created. (You know that big, solid gold menorah overlooking the Kotel plaza? That's theirs, and fit for use in the Temple.)
Naturally, as part of their efforts, they have created building plans.
As you can see on a post on their IndieGogo campaign (find the one titled "ARCHITECTURAL PLANS FOR HOLY TEMPLE SANCTUARY INAUGURATED"; i'm unable to directly link to it.), they are using fully modern architectural planning, computerized blueprints and all.
They also have a computer-generated video of what the Chamber of Hewn Stone (לשכת הגזית) (the Sanhedrin's place) would look like.
You can also look at their blueprints on their site.
Not only do they plan on using technology to design and build it, but they also want to have a "fully modern third Temple, Kosher to the letter of the law but including modifications like underground parking, heating and computerized washing stations that minimize water waste."[source]
Also: "While strictly adhering to the religious requirements set forth in Biblical texts, the Third Temple will also be equipped with every modern amenity: full computerization, underground parking, temperature control, elevators, docks for public transportation, wheelchair access, and much more."[source]
According to this source, 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.)