The press blurb for “A Cooler Climate,” a 75-minute documentary from veteran director and writer James Ivory, calls it “deeply personal,” but this is a relative term in his case. At 94 years of age, Ivory is an extraordinarily reticent man, and that is partly a result of being born in a certain time and place. There is only so much he can or will reveal about himself before retreating and closing several doors firmly behind him.

The impetus behind “A Cooler Climate” was the chance to showcase color footage that a young Ivory shot in Afghanistan in 1960 with the idea of making a documentary. This was a few years before he made his first narrative feature with his longtime partner and producer Ismail Merchant, with whom he eventually made a series of prestigious literary adaptations in the 1980s and 1990s with screenplays by Ruth Prawer Jhabvala.

Ivory’s literary adaptations...