The best manure is livestock dung mixed with bedding. The amount of nourishment that manure supplies to a plant during the first season depends on the ratio of bedding to dung. More bedding means less nourishment to plants the first season, but a greater residual effect for subsequent seasons. The heat comes from the burst of microbial activity stimulated by these manures' relatively high concentrations of nitrogen and low concentrations of water. Never use dog or cat manure in the garden because these can transmit diseases to humans.
Most gardeners dig it into the soil immediately.
If the manure is well-rotted, with the bedding material no longer recognizable, planting can begin when the soil is smoothed. If the manure is relatively raw, wait at least two weeks before planting. You also could just lay manure on top of the ground as mulch. This is fine if the manure is rotted, but nitrogen escapes as gas from fresh manure exposed to sun and wind. The nitrogen loss is wasteful, but it may be worth the sacrifice considering the benefits of the mulch.