The transient electrothermal technique has been shown to be an important method for the thermal characterization of fine fibers. However, this study shows that the accuracy of this method hinges on the proper consideration of several sample parameters including the initial electrical resistance and the emissivity of the sample. Such consideration is verified through measurement of platinum samples with various lengths. A multi-level heating scheme is proposed to mitigate the high sensitivity to the initial sample electrical resistance resulting in a demonstrated precision uncertainty of <3% Using a recently expanded thermal model accounting for heretofore neglected heat losses, the emissivity of the sample may be measured simultaneously with thermal conductivity. The influence of the vacuum level is demonstrated by the results of measurements at two vacuum levels <0.001 Pa (diaphragm plus turbo pumps) and ~2 Pa (regular rotary vane pump). Neglecting these considerations can produce seemingly viable measurement results having significant bias error. Based on the characteristics of the expanded model, a new approach is presented that takes advantage of the simplicity of the reduced model, which neglects lateral heat losses from the sample, to obtain sample thermal properties that are independent of heat loss effects. Lastly, several experimental results validate the new model.