Notwithstanding the success of polymer-carbon nanotube (CNT) nanocomposites, a solid understanding of the impact of external perturbations, including temperature and stress, on the electrical response, its reproducibility, and the subsequent relationship to the topology of the percolative morphology and molecular details of the CNT-CNT contact junction is not complete. Using an in situ synthesis approach, two series of polymide (CP2)-carbon nanofiber (CNF) composites are prepared with quantitatively (small-angle X-ray scattering) comparable CNF dispersions, but differing in the structure of the CNF-polymer interface. Amino-functionalized CNFs (FCNFs) enable direct formation of CP2 grafts onto the CNFs, whereas pristine CNFs (PCNFs) result in a relatively weak interface between the carbon nanofiber and CP2 matrix. In general, low-frequency ac impedance measurements are well described by the percolation bond model, yielding a percolation threshold below 1 vol % (0.24 and 0.68 vol % for PCNF-CP2 and FCNF-CP2, respectively). However, the design of the interface is determined to be crucial for controlling the electrical behavior in four substantial ways: magnitude of the limiting conductivity, linearity of the I-V response, magnitude and direction of temperature-dependent resistivity, and reproducibility of the absolute value of the resistivity with thermal cycling. These observations are consistent with a direct CNF-CNF contact limiting transport in the PCNF-CP2 system, where the CP2 grafts onto the FCNF from a dielectric layer, limiting transport within the FCNF-CP2 system. Furthermore, the grafted CP2 chains on the FCNF reduce local polymer dewetting at the CNF surfaces when the temperature exceeds the CP2 glass transition. This appears to stabilize the structure of the percolation network and associated conductivity. The general behavior of these interfacial extremes (pristine and fully functionalized CNFs) set important bounds on the design of interface modification for CNFs when the intended use is for electrical performance at elevated temperatures or under extreme current loads.