Narrow pore / fracture pressure gradient margins (operating window) is translated as a real drilling hazard scenario, where a slight change in the bottom hole pressure conditions can lead to an increase the Non Productive Time (NPT) due to the time spent in solve a possible fluid losses and/or gas kick situation, or even worst, dealing with occurrence of blowouts. In specific and non rare cases, deep formations with small gap between pore and fracture pressure are un-drillable with conventional drilling practices because the frictional losses pressure (difference between the dynamic and static pressure) is greater than the existent operating window. Constant Bottom Hole Pressure (CBHP), one of a number of variants of Managed Pressure Drilling (MPD) enables "walking the line" between pore and fracture pressure gradient. The objective is to drill with a fluid that bottom hole pressure is maintained constant, whether the fluid column is static or circulating. The loss of annulus flowing pressure when not circulating is counteracted by applied surface backpressure. The basic of Constant Bottom Hole Pressure (CBHP) methodology is to accurately determine the change in bottom hole pressure caused by dynamic effects and compensate with an equal change in annular wellhead pressure. The bottom hole temperature as well as the hydrostatic head of the drilling fluid column increases with the well depth and both parameters have opposing effect in the resultant static and dynamic equivalent density. An increase in the hydrostatic and dynamic pressures increases the equivalent fluid density due to compression but an increase in the temperature causes a reduction in the equivalent fluid density due to thermal expansion. Conventionally, these parameters considered together results in a cancellation of effects. In the reality, this assumption should be carefully reviewed. The effect of temperature in annular pressures, on a MPD CBHP operation through narrow operating windows, can not be ignored due to the potential impact. Precise estimation of static and dynamic equivalent fluid densities is of essential importance for a successful MPD CBHP operation through narrow operating windows.