In this study we investigate mixing under transcritical conditions by means of direct numerical simulation. A temporal jet configuration is used together with thermodynamic conditions matching those of experiments on cryogenic injection of nitrogen at supercritical pressures. Two cases, representing supercritical and transcritical conditions, are simulated using a spectral element based, low-Mach number flow solver, coupled with detailed real-fluid equation of state and transport properties. The objective is to shed light on the transcritical mixing process and to concurrently investigate, in a-priori fashion, the sub-grid scale modeling of thermodynamic and transport properties in the context of large eddy simulation. Relevant qualitative and statistical differences between supercritical and transcritical jets are observed, despite the same initial Reynolds number. The use of a presumed beta-pdf for sub-grid scale mixing is investigated and is shown to significantly improve, with respect to the largely used "no-model", the evaluation of thermodynamic and transport properties.