This is the summit baggers route, the simplest and most obvious way for someone to gain the summit of Minerva's Temple. Unlike the nearby summits, this one requires technical climbing abilities and gear, even if it is only for a single pitch.
Starting from the gap between the Retaining Wall and Minerva's Temple the route takes an obvious weakness directly on the west end of the ridge. After climbing up 30 ft, the corner can be turned over onto the south wall where a small bush impedes prgress along a sloping foot-ledge. Several nice crack systems lead straight up to the ridge-top from this foot-ledge and provide more difficult variations (5.9-5.10 range). Skip over these crack systems and traverse right until a difficult move is required to traverse into an easy corner system (crux move, exposed). Easy climbing straight up on the face gains the summit ridge.
From the summit ridge, scramble for ~200 ft to the east to a small col with Aspen trees. From here a short 40 ft pitch gains over some technical blocks gains the summit.
The route starts on the west end of the peak, in a gap between it and the Retaining Wall of Organ Needle. This can be approached best from the west. The easiest approach is to hike the Organ Needle trail all the way to Hummingbird Saddle, and then descend the maple filled canyon on the east until you can gain the gap. Done this way, one must climb up to the gap, either straight up for 75ft or by traversing in to the gap (both 5th class). Alternatively, one can approach by skirting around the south side of the Retaining Wall or by coming up directly from Fillmore canyon to the south.
Descend by reversing the route. A single short rappel gets off the summit. From a point on the far west end of the ridge, a single rappel can just barely reach the gap. Place your rappel as low as possible on the ridge.
A light alpine rack is adequate. Bring a few long pieces of webbing and leaver biners or rap-rings as fixed rappel equipment is un-likely to be found.