  In the increasingly active field of optofluidics, a series of experiments
involving near-critical two-fluid interfaces have shown a number of interesting
non-linear effects. We here offer, for the first time to our knowledge, an
explanation for one such feature, observed in experiments by Casner and
Delville [Phys. Rev. Lett. {\bf 90}, 144503 (2003)], namely the sudden
formation of "shoulder"-like shapes in a laser-induced deformation of the
liquid-liquid interface at high laser power. Two candidate explanations are the
following: firstly, that the shape can be explained by balancing forces of
buoyancy, laser pull and surface tension only, and that the observed change of
deformation shape is the sudden jump from one solution of the strongly
nonlinear governing differential equation to another. Secondly, it might be
that the nontrivial shape observed could be the result of temperature gradients
due to local absorptive heating of the liquid. We report that a systematic
search for solutions of the governing equation in the first case yields no
trace of solutions containing such features. By contrast, an investigation of
the second option shows that the narrow shape of the tip of the deformation can
be explained by a slight {\it heating} of the liquids. The local heating
amounts to a few kelvins, with the parameters given, although there are
uncertainties here. Our investigations suggest that local temperature
variations are the crucial element behind the instability and the shoulder-like
deformation.
