A novel approach to study electron thermal transport in dense plasmas was successfully implemented to measure the temperature-dependent conductivity and test the currently available dense plasma model by Lee and More. Intense, femtosecond laser pulses with energy up to 7 mJ per pulse were used to heat free-standing 170-370 nm aluminum foils. We carried-out a new approach to study the plasma transport properties of electron and thermal conduction. In this new approach, rather than probing the front (laser-heated) surface, probing was done on the back surface of a thicker metallic foil heated by a thermal conduction wave generated from a laser-heated front surface. Frequency-domain interferometry with chirped probe pulses allowed us to simultaneously measure the time-dependence of the optical reflectivity and phase-shift in a single shot with subpicosecond resolution. In addition, solid heating was observed to be dominated by the thermal conduction wave prior to the shock-wave breakout at the back surface when laser energy was directly deposited in a thin metallic foil. As a result we were able to estimate the optical conductivity of a dense aluminum plasma in the range of 0.1 – 1.5 eV. The optical parameters were calculated using the output of a hydrodynamic simulation along with the published models of bound electron contributions to the conductivity and were found to be in reasonable agreement with the measurement. We found that the Lee and More model of a dense plasma’s conductivity predicts the real and imaginary part of the measured optical conductivity to within 20%. The simulation results were then used to examine the temperature dependence of the conductivity for 170 and 230 nm aluminum foils heated with the 2-5 mJ pulses. In all cases the same conductivity was obtained, though the arrival of the heat wave and subsequent shock waves varied with the choice of intensity and target thickness. This consistency in the data gave us good confidence in the validity of this technique for deriving conductivity as a function of temperature.