The swampy heat swaddles everything like a wet diaper. The coffee-colored Sekonyer River looks tempting to cool off in, but then there are the crocodiles and the water snakes. Somewhere out there, too, are rumors of headhunters — and not the business kind.

Instead, my family and I decide to kick back and let the orangutans in Borneo’s Tanjung Puting National Park come to us.

The park is one of the best places in the world to see the endangered orangutan in the wild. With South Asia’s tropical forests rapidly disappearing, particularly in Borneo, it’s also one the of only places where you can still see the great apes in their natural habitat.

To reach the park, we fly to Indonesia’s Central Kalimantan province from Jakarta, then take an old African Queen-style wooden boat from the port of Kumai on the Java Sea. We plop ourselves in deck chairs as the boat slowly putt-putts away from Kumai’s fishing shacks, cargo sheds and bright blue mosque, wheezes past freighters and canoes, and finally enters a channel leading to the jungle. Here, an unexpected billboard featuring a large picture of a big-eyed orangutan announces the entrance to the park.

Other than in the picture, though, the orangutans are initially hard to spot. Although the rain forest presses close on both sides of the boat, the apes stay hidden.

Our guide helpfully instructs us to look for swaying branches up in the canopy and for nests made of sticks: This is because orangutans are tree-dwellers, in fact the largest tree-dwelling mammals in the world.

We also learn to look in front of the boat, rather than to the side, and soon we spot moms with babies firmly attached swinging from tree branch to tree branch or munching contentedly on fruit. At ground level, I see solitary males, with their telltale large, leathery cheek pads, along the reedy banks. Most are drinking from the river or scavenging for food. Scientists have found that some of the park’s apes use sticks to spear fish, but the orangutans near us are stickless.

I spot one big male squatting in the mud, oblivious to the boat but riveted by a stray soda can. Slowly, he turns the can end over end, trying to divine its shiny purpose. Then, finding the top, he pops open the tab and, to his considerable surprise, sprays himself in the face. Those opposable thumbs can be a mixed blessing, I suppose.

Farther along, less shy orangutans, both moms with babies and solitary males, watch the boat from branches close to the shore. Our guide calls to the animals, whistling and making kissing sounds. The orangutans remain silent but cautiously swing closer to the boat. A few venture to waterside branches, although the park discourages visitors from getting too close for safety (the 250- to 300-pound males can be dangerously unpredictable) and health reasons.

I tentatively hold out a banana to one mom and, standing face to face with her, suddenly feel an easy kinship with the great ape. Not surprising, since they share 97 percent of our DNA. Our guide tells us that the word “orangutan” derives from a Malay word meaning “forest man.”

Gibbons, macaques and big-bellied, big-nosed proboscis monkeys (which locals call Dutch monkeys after the island’s former colonial overlords) also wait to join in on the banana mother lode and peer curiously from nearby trees. Somewhere in the forest, too, are clouded leopards, sun bears and pygmy elephants, but these animals are too savvy to let us see them, and for good reason. Humans haven’t been so kind to the rain forest and its denizens in recent decades.