This paper presents an in-depth study of the design, modelling, circuit parameter extraction and characterization of a distributed MEMS digital microwave phase shifter. Bridge-type digital capacitors periodically loaded on a 5 mm CPW (with an actuation voltage of 22 V) has been fabricated and successfully measured in a wide range of frequencies (1-14 GHZ), achieving a true-time delay of 25 ps. Experimental data are in very good agreement with the equivalent circuit model and high frequency 3D EM simulations for both single switches and phase shifters. These phase shifters are designed for beam steering applications in airborne and space which require operation within large range of temperatures. Therefore, temperature measurements fulfilling the applications requirements have been done in vacuum and in room air from -130degC to 50degC. It is demonstrated that the delay deviation of our phase shifter is 10% (2 ps) at 14 GHz for the full temperature range (DeltaTdeg=180deg).