Using spectral analysis we have studied changes in the heart rate during periodic thermal stimulation of one foot of infants during quiet sleep. Twenty-two appropriately grown preterm infants were studied in the first 15 d after birth to quantify responses in comparison with previously reported term infants. Babies were stimulated at 0.05, 0.10, and 0.15 Hz. Spectral power was calculated at the stimulus frequency +/-0.01 Hz and +/-0.02 Hz and over the low frequency range 0.03 Hz to 0.17 Hz. The data show that 1) there is an increase in power around the frequency of stimulation for each frequency studied (p < 0.002); and 2) there is an increase in the ratio of local to low frequency power at 0.05 Hz (p = 0.002) and 0.10 Hz (p = 0.001), but not at 0.15 Hz (p = 0.109). These data confirm the concept of entrainment in the appropriately grown preterm infant but demonstrate that it occurs over a wider frequency range than previously reported. The wider range is the same as that of the term infant, although there are differences in the patterns of entrainment between the two groups. Further work is required to map out the maturation of the autonomic nervous system in both the term and the preterm infant with respect to the low frequency components of the heart rate variability power spectrum.