We analyze the fluctuations of an electronic thermal current across an idealized molecular junction. The focus here will be on the spectral features of the resulting heat fluctuations. By use of the Green functionmethod we derive an explicit expression for the frequency-dependent power spectral density of the emerging energy fluctuations. The complex expression simplifies considerably in the limit of zero frequency, yielding the noise intensity of the heat current. The spectral density for the electronic heat fluctuations still depends on the frequency in the zero-temperature limit, assuming different asymptotic behaviours in the low- and high-frequency regions. We further address subtleties and open problems from an experimental viewpoint for measurements of frequency-dependent power spectral densities.