The present invention provides a process of producing unsaturated acids from unsaturated aldehydes by fixed-bed catalytic partial oxidation in a shell-and-tube heat exchanger-type reactor, as well as a shell-and-tube heat exchanger-type reactor for use in the process. In the invention, second-stage reaction zone of mainly producing unsaturated acids by the catalytic vapor phase oxidation of an unsaturated aldehyde-containing gas mixture produced in a first-stage reaction zone with molecular oxygen is divided into two or more shell spaces by at least one partition. Each of the divided shell spaces is filled with a heat transfer medium, and the heat transfer medium in each shell space is maintained at isothermal temperature or a temperature difference of 0-5° C. Also, in order to protect catalyst layers from a highly exothermic reaction, the process is performed at a limited temperature difference between the temperature at a hot spot and the temperature of the heat transfer medium. Also, in order to facilitate the removal of heat generation at a location where the partition is placed, a reaction inhibition layer is disposed in that location. The improved heat control system for reactors provided according to the present invention can secure the heat stability of the catalyst layer, reduce the amount of byproducts, and increase the yield of a final product.