Which type of animals will most likely be supported in an environment that has a high temperature and rainfall year round?
"High temperature and rainfall year-round" describes the tropical rainforest biome. Tropical rainforests are recognized as supporting the largest diversity of animal life known to science, including a huge array of anthropod species, as well as many vertebrates, including small mammals, birds, and amphibians.
In some cases, the moisture and high temperatures of the tropical rainforest have a direct influence on what types of animals live there. For instance, frogs require moist, warm conditions, and there is a high diversity of frog species in the tropics.
But the kinds of animals we observe in this biome also reflect the plant life: The abundance of leaves, fruit, and seeds means there are many ecological niches open for exploiting these foods. Thus, we see the types of animals that make their living from those plant foods.
For example, folivorous (leaf-eating) species include the larval and adult feeders of Lepidoptera (moths and butterflies), Coleoptera (beetles), Hymenoptera (ants and their relatives). There are also many vertebrate folivores, like the howler monkeys of Central and South America, and various leaf-eating marsupials.
Frugivorous (fruit-eating) animals include parrots, certain monkey species (like spider monkeys in the New World tropics), and fruit bats.
In addition, there are opportunistic omnivores, like coatis (in the New World), capuchin monkeys (in the New World) and civets (in Asia). And of course there are predators at the top of the food chain, like harpy eagles and jaguars (of the Amazonian rainforest) and tigers and leopards (in India).