Context : Photoelectric heating is a dominant heating mechanism for many phases of the interstellar medium .
We study this mechanism throughout the Large Magellanic Cloud .

Aims : We aim to quantify the importance of the [ C II ] cooling line and the photoelectric heating process of various environments in the LMC and to investigate which parameters control the extent of photoelectric heating .

Methods : We use the BICE [ C II ] 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 , i.e .
the observed [ C II ] line strength over the integrated infrared emission .
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 .
The observed variations are interpreted in a theoretical framework .
From this we estimate radiation field , gas temperature , and electron density .

Results : 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 ( \sim 1.4 times lower ) .
The [ C II ] line emission constitutes 1.32 % of the far infrared luminosity across the whole of the LMC .
We find correlations between the [ C II ] 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 _ { \mathrm { TIR } } , the [ C II ] surface brightness can be described as : \mathrm { S _ { \mathrm { [ { C \textsc { II } } ] } } = 1.25 \leavevmode \nobreak S _ { \mathrm { TIR } % } ^ { 0.69 } \leavevmode \nobreak [ 10 ^ { -3 } \leavevmode \nobreak erg \leavevmode% \nobreak s ^ { -1 } cm ^ { -2 } sr ^ { -1 } ] } , for \mathrm { S _ { \mathrm { TIR } } \leavevmode \nobreak \gtrsim \leavevmode \nobreak 3.2 % \cdot \leavevmode \nobreak 10 ^ { -4 } erg \leavevmode \nobreak s ^ { -1 } cm ^ { -2 } sr ^ { -1 } } .
We provide a simple model of the photoelectric efficiency as a function of the total infrared .
We find a power-law relation between radiation field and electron density , consistent with other studies .
The [ C II ] emission is well-correlation with the 8 \mu m emission , suggesting that the polycyclic aromatic hydrocarbons play a dominant role in the photoelectric heating process .

Conclusions :