The magnetic structure within circular chains composed of 30-nm-diameter, polymer-coated nickel particles was studied by electron holography. The magnetic flux closure due to dipolar coupling was confirmed at zero external magnetic field. Its long-range order parameter was determined from the magnitude of the electron phase shift, and it was found to decrease more rapidly than that of bulk nickel as a function of temperature. The results of Monte Carlo simulations indicated that the temperature variation of the order-parameter was explained in terms of weakened dipolar coupling field ascribed to the decay of the bulk magnetization and enhanced thermal fluctuations.