The experimental achievement of reacting two phases that are held at two different temperatures - the anisothermal reaction condition-is a radical innovation in materials chemistry. Details on the synthesis of Yttrium Iron Garnet (Y3Fe5O12), Barium Ferrite (BaFe12O19), and Nickel Aluminate (NiAl2O4) in 1-10 min in a microwave field are provided. The starting precursor oxides were chosen such that they include a low and a high microwave absorbing phases. When these mixtures are exposed to a 2.45-GHz multimode microwave field the highly absorbing powder particles act as (micro)heat sources and the low absorbing powder particle act as (micro)heat sinks, and create the "anisothermal heat distribution," a hitherto never attained phenomenon in materials science. A comparison study carried out comparing conventional reactions of the same phases suggested that the "anisothermal heating phenomenon" is also responsible for the very rapid reactions and product formations. Model experiments performed with an Y2O3/Fe3O4 diffusion couple showed a unidirectional diffusion of Fe species into Y2O3, forming a different sequence of intermediate phases.