The effects of heat treatment and the addition of tarragon essential oil on physical and mechanical properties of films prepared with 5% whey protein isolate (WPI) and 5% glycerol were investigated in this study. Heat treatment of the film-forming solution caused increases in thickness, moisture content, swelling degree, water vapor permeability (WVP), b*-value, ΔE*-value, transmittance values in the 200–300-nm region, transparency, and puncture resistance of the film, but decreases in water solubility, L*-value, a*-value, transmittance values in the 350–800-nm region, and puncture deformation. When incorporated with tarragon essential oil, heat-treated films have the potential to be used as antimicrobial food packaging. The addition of tarragon essential oil in film-forming solution caused increases in moisture content, solubility in water, WVP, a*-value, b*-value, ΔE*-value, and transparency of the film; decreases in transmittance values in the range of 600–800 nm; and variations in swelling degree, L*-value, transmittance values in the range of 300–550 nm, puncture resistance, and puncture deformation. Nevertheless, different tendencies were noticed in UNT (untreated) and HT (heat-treated) films with regards to transparency, light transmittance, puncture resistance, and puncture deformation. Based on these findings, HT films show improved physical and mechanical properties and, therefore, are more suitable for food-packaging applications.