Mulching around established woody plants is all right as long as the mulch is a little less thick around them. The composting should be a slow burn. It will get warm to some extent, but should not actually be noticeable to us humans. The energy will feed the multitudes of micro and macro fauna and flora that will then be able to build the soil structure. If the layer is warm inside, reduce its thickness and water it.
Soil structure is the key to a healthy soil.
Soil structure is a full range of pore sizes that are lined with the proteins, sugars and fats of the microbes and their actual bodies. These passages into the soil profile allow for water, nutrient and gas movement, creating ideal conditions to support plants. Always keep the soil covered. Do not pile it on top of shrubs, but you can place it up against tree trunks. Occasionally, a thick layer of mulch may grow a facultative fungus that can eat dead or living tissue.