More than 40 years ago, DNS (Direct Numerical Simulation) started with the pioneering work of Orszag . This powerful workbench to study turbulence is attracting rising numbers of researchers as the computational power available increases. However, few DNS have dealt with conjugate heat transfer issues. Tiselj et al.  were among the first to investigate this more realistic situation in a channel flow using pseudo-spectral methods. Kang et al.  performed Quasi-DNS with conjugate heat transfer of a heated cylinder in a channel using immersed boundaries and fully implicit LES solver based on unstructured collocated mesh.Conjugate heat transfer is a major issue in industrial applications where cooling of hot components is often critical. In complex situations, RANS and LES simulations rely on wall-function modelling as the viscous sub-layer is not resolved. DNS is a valuable tool for understanding the flow physics of such complex phenomena and to provide fine data in order to improve RANS and LES approaches.This document summarizes the developments performed in the open-source DNS code Incompact3d to investigate conjugate heat transfer. Budgets of second-order statistics for a channel flow with different thermal boundary conditions are presented (imposed temperature, imposed heat flux and conjugate heat transfer). To the author's knowledge, budgets for imposed heat flux and conjugate heat transfer are not available in the literature. Such data is valuable in the scope of assessing accuracy of wall-modeling.