Context : The XXL Survey is the largest homogeneous survey carried out with XMM-Newton .
Covering an area of 50 deg ^ { 2 } , the survey contains several hundred galaxy clusters out to a redshift of \approx 2 above an X-ray flux limit of \sim 5 \times 10 ^ { -15 } erg cm ^ { -2 } s ^ { -1 } .
This paper belongs to the first series of XXL papers focusing on the bright cluster sample .

Aims : We investigate the luminosity-temperature ( LT ) relation for the brightest clusters detected in the XXL Survey , taking fully into account the selection biases .
We investigate the form of the LT relation , placing constraints on its evolution .

Methods : We have classified the 100 brightest clusters in the XXL Survey based on their measured X-ray flux .
These 100 clusters have been analysed to determine their luminosity and temperature to evaluate the LT relation .
We used three methods to fit the form of the LT relation , with two of these methods providing a prescription to fully take into account the selection effects of the survey .
We measure the evolution of the LT relation internally using the broad redshift range of the sample .

Results : Taking fully into account selection effects , we find a slope of the bolometric LT relation of B _ { LT } =3.08 \pm 0.15 , steeper than the self-similar expectation ( B _ { LT } =2 ) .
Our best-fit result for the evolution factor is E ( z ) ^ { 1.64 \pm 0.77 } , fully consistent with “ strong self-similar ” evolution where clusters scale self-similarly with both mass and redshift .
However , this result is marginally stronger than “ weak self-similar ” evolution , where clusters scale with redshift alone .
We investigate the sensitivity of our results to the assumptions made in our fitting model , finding that using an external LT relation as a low-z baseline can have a profound effect on the measured evolution .
However , more clusters are needed in order to break the degeneracy between the choice of likelihood model and mass-temperature relation on the derived evolution .

Conclusions :