A kind reader, Joseph Adler of Kenyon College, has helped me out:

Here is a pretty good Wade-Giles to Pinyin conversion table. The “major differences” listed at the top should really be enough.

A rule that could be added is that the apostrophe indicates aspiration. Since the only difference between the k and g sounds in English is that k is aspirated while g is voiced, k’ in W-G sounds like our (and pinyin’s) k, while k (no apostrophe) in W-G sounds like our g. The same is true for all the W-G consonants that take the apostrophe.

Thus, the two temples are Jie Tai Si and Dan Jue Si (also written, I notice, as Tan Zhe Si, to add to the confusion). But I’ve found them online, with photos (and “luxury tours” offered), and can now read about them in my various Beijing and China guides. I will be visiting various places in China in August/September (for the Beijing International Book Fair and meetings with contributors to Guanxi: The China Letter, and these temples will be top on my list for non-business time in Beijing. I won’t be doing a luxury tour, though, and hope to get a Chinese friend to go with me. When I first went to China in 2001 with my husband and children, we used no tour guides after the first day. We found a taxi driver to take us wherever we were going, and I intend to do the same. Admittedly, we were a bit nervous on occasion, especially the time we set off for Heaven Lake from the city of Urumchi in western China. I’d repeatedly said “Tian Shan” to the driver and showed him a tiny map in my guidebook, but we were not positive he understood. Our anxiety was heightened when the hotel doorman waved a cheerful good-bye and said, “Hoping to see you again some day.”