A multi-tubular reaction apparatus, a control system, and a method are provided for controlling temperature change of a heat medium in the reaction apparatus, and quickly adjusting fluctuation in temperature, to thereby properly control a reaction. In particular, the apparatus and system apply to a catalytic gas-phase oxidation reaction such as in producing (meth)acrylic acid or the like. The reaction apparatus includes a multi-tubular reactor having a plurality of reaction tubes in a shell in which a heat medium circulates, and a heat medium cooling apparatus outside the reactor. The reaction apparatus includes a process for primarily cooling the heat medium taken out outside the shell, a process for secondarily cooling a part of the primarily cooled heat medium, and a line for enabling the secondarily cooled heat medium and the primarily cooled heat medium, which is not secondarily cooled, to circulate in the shell.