Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with constant heat flux for which the value is negative for no-slip flow. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian method. The computations are performed for channels with constant heat flux ranging from -10(4) to -10(2) W/m(2). The channel height ranges from 10 to 100 mu m and the aspect ratio of the channel height and length is 200. The stagnation pressure is chosen such that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in micro-channels with negative heat flux are compared with those of positive heat flux cases obtained in our previous work and also those of the incompressible flow in a conventional sized channel. In the case of fast flow, temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the micro-channel is proposed. The rarefaction effect is investigated for the cases of channel height of 10 mu m with slip boundary conditions. The magnitudes of viscous dissipation term and compressibility term are also investigated. The effect of each term on heat transfer characteristics is discussed.