  (abridged) We study photoelectric heating throughout the Large Magellanic
Cloud. We quantify the importance of the [CII] cooling line and the
photoelectric heating process of various environments in the LMC and
investigate which parameters control the extent of photoelectric heating. We
use the BICE [CII] map and the Spitzer/SAGE infrared maps. We examine the
spatial variations in the efficiency of photoelectric heating: photoelectric
heating rate over power absorbed by grains. We correlate the photoelectric
heating efficiency and the emission from various dust constituents and study
the variations as a function of H\alpha emission, dust temperatures, and the
total infrared luminosity. From this we estimate radiation field, gas
temperature, and electron density. We find systematic variations in
photoelectric efficiency. The highest efficiencies are found in the diffuse
medium, while the lowest coincide with bright star-forming regions (~1.4 times
lower). The [CII] line emission constitutes 1.32% of the far infrared
luminosity across the whole of the LMC. We find correlations between the [CII]
emission and ratios of the mid infrared and far infrared bands, which comprise
various dust constituents. The correlations are interpreted in light of the
spatial variations of the dust abundance and by the local environmental
conditions that affect the dust emission properties. As a function of the total
infrared surface brightness, S_{TIR}, the [CII] surface brightness can be
described as: S_{[CII]}=1.25 S_{TIR}^{0.69} [10^{-3} erg s^{-1} cm^{-2}
sr^{-1}]. The [CII] emission is well-correlation with the 8 micrometer
emission, suggesting that the polycyclic aromatic hydrocarbons play a dominant
role in the photoelectric heating process.
