Enhancing skin permeation is important for development of new transdermal drug delivery formulations. This is particularly relevant for non-steroidal anti-inflammatory drugs (NSAIDs). To address this, semisolid gel and solid hydrogel film formulations containing gellan gum as a gelling agent were developed and the effects of penetration enhancers (dimethyl sulfoxide, isopropyl alcohol and propylene glycol) on transport of the NSAID diclofenac sodium was quantified. A transwell diffusion system was used to accelerate formulation development. After 4 h, diclofenac flux from a superior formulation of the semisolid gel or the solid hydrogel film was 130 ± 11 μg/cm2 h and 108 ± 7 μg/cm2 h, respectively, and significantly greater than that measured for a currently available diclofenac sodium topical gel (30 ± 4 μg/cm2 h, p < 0.05) or solution formulation (44 ± 6 μg/cm2 h, p< 0.05) under identical conditions. Over 24 h diclofenac transport from the solid hydrogel film was greater than that measured for any new or commercial diclofenac formulation. Entrapment of temperature-responsive nanogels within the solid hydrogel film provides temperature-activated prolonged release of diclofenac. Diclofenac transport was minimal at 22 °C, when diclofenac is entrapped within temperature-responsive nanogels incorporated into the solid hydrogel film, but increased 6-fold when the temperature was increased to skin surface temperature of 32 °C. These results demonstrate the feasibility of the semisolid gel and solid hydrogel film formulations that can include thermo-responsive nanogels for development of transdermal drug formulations with adjustable drug transport kinetics.