We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice and in the presence of thermal noise. The internal degree of freedom of each particle is a periodic variable that is coupled to those of other particles with an attractive XY-like interaction. The coupling strength decays with the interparticle separation r in space as 1/r^{α}; 0<α<1. We study the dynamics of the model in the continuum limit by considering the Fokker-Planck equation for the evolution of the spatial density of particles. We show that the equation allows a linearly stable stationary state, which is always uniform in space, being nonuniform in the internal degrees below a critical temperature T=1/2 and uniform above, with a phase transition between the two at T=1/2. The state is the same as the equilibrium state of the mean-field version of the model, obtained by considering α=0. Our analysis also allows us to compute the growth and decay rates of spatial Fourier modes of density fluctuations. The growth rates compare very well with numerical simulations.