The influence of low-temperature annealing, at < 360 degrees C, in various reducing and oxidizing atmospheres for a series of BaTiO3 ceramics with a positive temperature coefficient of resistance (PTCR) is discussed. Combined impedance and modulus spectroscopy is used to analyse a.c. impedance data and shows that the total resistance of the sample can be composed of up to three components, dependent on the cooling rate from the sintering temperature. For quickly cooled samples the PTCR response is dominated by an outer shell on individuals grains, whereas for slowly cooled samples the grain boundary resistance dominates. Annealing in reducing atmospheres destroys the grain boundary PTCR effect whereas the outer-shell grain PTCR effect is relatively insensitive to the reducing atmosphere. It is proposed that the acceptor states responsible for the outer-grain and grain-boundary PTCR effects are predominantly intrinsic metal vacancies, i.e. Ba and/or Ti, and adsorbed oxygen, respectively.