A method for improving a residual stress in a pipe includes improving the residual stress in the inner surface to the compressive direction by rapid cooling of the inner surface after heating of the pipe. The heating is to heat a vicinity of a welded part of the pipe from the outer surface to raise the temperature to a construction temperature. The rapid cooling is to rapidly cool the inner surface in the vicinity of the welded part by supplying cooling water into the pipe. The heating and the rapid cooling are repeated twice or more. A method for construction management includes determining whether construction has been executed properly based on a maximum value of a lowering rate of an outer surface temperature of the pipe when the cooling water is supplied for the rapid cooling of the inner surface and a thickness of the pipe in a measuring position of the outer surface temperature.