I just looked up how i did it. Once I got to Kyoto station, i immediately switched to the subway to karasuma-Oike, then to the subway to Higasi-yama. (both subways are very short rides)
It's all on the trip listed on the airport site as "higashi-yama"
I probably spent less than 10 minutes in Kyoto city itself. Went immediately to the temples that way.
By the way I did make one big mistake, which is when I got off the plane from bangkok I went upstairs (which transit passengers do). It was a big pain to get back downstairs to go through customs and i also then had to wait in line. It really ticked me off because though I arrived at like 7 a.m., I didn't leave kix til 9:30 cutting down my time in kyoto.
Whatever you do, don't make my mistake.