Cryogenic nitrogen jetting is a promising drilling rate improvement method, in which heat transfer plays an important role in inducing thermal stresses and facilitating rock breakage. In the present study, we aim to study flow field and heat transfer of a cryogenic nitrogen jet in two potential phase states (i.e. liquid and supercritical) under downhole conditions and determine the effect of some critical engineering parameters, including inlet pressure, ambient pressure and standoff distance, which are of concern for field applications of this method. Three different detached eddy simulation (DES) approaches were compared and validated to assess their performances in jet flow issues. These comparisons indicate IDDES showed better performance in predicting the flow field and heat transfer of jet flow, and thus was adopted for the present simulations. According to the simulation results, vorticity, dominant frequency fd of vortex instability and pressure oscillations grow with increasing inlet pressure for both free and impinging jets. Compared to the liquid nitrogen (LN2) jet, the supercritical nitrogen (SCN2) jet has higher vorticity magnitude and fd of temperature fluctuations, causing its vortex rings to breakdown in advance. The dominant frequency of temperature oscillations at the stagnation point falls at the same level as that of vortex instability in the shear layer, revealing the prevailing role of large-scale vortices in heat transfer. Under the same jet pressure condition, the heat transfer rate for SCN2 jet is constantly higher than that of LN2 jet. Increasing inlet pressure helps increase fd of temperature fluctuations and heat transfer rate for both LN2 and SCN2 jets. Under the same pressure difference (between inlet and outlet), lower ambient pressure is more conducive for SCN2 jets to enhance the vortex scale and heat transfer rate. In contrast, the ambient pressure has no significant influence on the LN2 jet. In the range of h/d ≤ 6, higher standoff distance delays the transition of vortex structures in the wall jet zone and contributes to the enhancement of heat transfer efficiency.