Thermal behavior of Coulomb clusters in a three dimensional confining potential is investigated by molecular dynamics simulations for system sizes of 1,000 to 20,288 ions. The specific heat of the system of shell-structured 20,000 ions is peaked almost at the same temperature as the system of bcc-structured 20,288 ions with much sharper structure for the latter. The diffusion coefficient and the peak to valley ratio of the two-dimensional pair distribution function on the outermost shell are obtained both as a function of temperature. The rotational movement of each shell in the system of 104 ions is observed.