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We investigate the finite-temperature excitation spectrum in the gluon sector of SU (3) pure gauge theory through measurements of screening masses in correlations of loop operators. We develop the classification of such operators under the symmetry group of the “z-slice”. In the confined phase of the theory, we find that the spectrum dynamically realizes the zero-temperature symmetries. We observe a large thermal shift of the 0++ glueball mass. In the deconfined phase, the spectrum distinguishes between operators coupling to electrically and magnetically polarised gluon fields. The former yields a screening mass equal to the Wilson-line screening mass; the latter a method for the measurement of the magnetic mass in the high-temperature limit.