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Thermotransmission and thermoreflection measurements were made on semitransparent films of Al, Au, and Cu at about 370 and 120 K in the range 0.5-5 eV. The data yield the thermomodulation spectrum Δε2 of the imaginary part of the dielectric constant directly, without Kramers-Kronig analysis. A comparison of the interband region of Δε2 for Cu with the piezo-modulation spectrum of a single crystal shows that broadening of the Fermi distribution and volume strain caused by thermal expansion are the principal causes of the Δε2 spectrum. The Δε2 spectrum for Al is particularly simple and can be discussed using closed-form expressions for the optical conductivity. It appears that the temperature dependence of the interband relaxation time for transitions across gaps produced by |V111| is smaller than that for transitions across gaps caused by |V200|, which in turn is smaller than that for the infrared intraband transitions.