We report on an experimental investigation of temporal, scalar power spectra of round, high Schmidt number (Sc cz 1.9 x lo3), momentum-dominated turbulent jets, for jet Reynolds numbers in the range of 1.25 x lo4 < Re < 7.2 x lo4. At intermediate scales, we find a spectrum with a slope (logarithmic derivative) that increases in absolute value with Reynolds number, but remains less than 5/3 at the highest Reynolds number in our experiments. At the smallest scales, our spectra exhibit no k-' power-law behaviour, but, rather, seem to be approximated by a log-normal function, over a range of scales exceeding a factor of 40, in some cases.