Yes, Koyasan -> Mount Koya is at Wakayama prefacture. There are over a hundred temples there and half of them let you stay. I stayed there for a few days and spent time and meditated with the generous monks. I guess the whole temple complex is also referred as Kongobuji temple.Is it the temple up on the mountain in Wakayama? That one was also wonderful.
The temple you are referring most probably is Kongobuji. The main temple/hall was called "Kondo"!
You have reminded of very beautiful times, thank you.