Heat affects the speed of the Maillard reaction, unlike a pyrolitic reaction (like caramelization) which can only happen above a certain temperature. (Sucrose and glucose both start to caramelize at 160C/320F, for example, while fructose will caramelize at 110C/230F.)
The Maillard reaction is a chemical reaction between an amino acid (eg, a protein) and a reducing sugar. All monosaccharides (like glucose and fructose) are reducing sugars, some disaccharides like sucrose and some polysaccharides are also reducing sugars.
As noted, it can occur at lower temperatures, but it will happen much faster in meat at temperatures above about 140C/285F. At even higher temperatures, pyrolitic reactions like caramelization are likely to overwhelm the effects of the Maillard reaction.
A low pH (ie, an acid) can inhibit the Maillard reaction, as can the presence of water.
The browning of a bread crust is a combination of the Maillard reaction and other reactions, especially caramelization.
Caramelization is another fascinating process, one that has not been heavily studied. Researchers have identified over a thousand compounds that can form when sugar (sucrose) is caramelized.