Provided are a fluid agitation apparatus using a structure which is simple in shape and short in a fluid passage direction without a movable part so as to produce a sufficient effect from the viewpoint of reducing temperature fluctuation, and a thermostatic apparatus using the fluid agitation apparatus. The fluid agitation apparatus is installed in a fluid passage and includes, in an order from an upstream side thereof: a dividing part for dividing a flow of a fluid into a plurality of flows; a circumvolving part for circumvolving the fluid about an axis in a flow direction of the fluid; and an accelerating part for increasing a flow rate of the fluid.