In this paper, a new 3-axis micromachined convective accelerometer is designed using restrictions of both 0.35 µm CMOS technology and front-side bulk micromachining (FSBM) post-process. Finite element modeling (FEM) is carried out using a validated 3D model to investigate the microsensor sensitivity as a function of power consumption. The proposed design includes a hollow square heater frame with four micro-heating resistances in each corner, and a new structure for the detector bridges. The allowed minimum oxide width is used for the micro-bridges to minimize heat loss. A comparison with a CMOS MEMS convective accelerometer from literature shows the superiority of the new design in terms of trade-off between sensitivity and power consumption. Better sensitivities along the three axes are obtained for lower heating temperatures, allowing the sensor to use higher heating powers to reach higher sensitivities. Moreover, higher sensitivities are found with the same heating power, offering higher efficiencies in terms of sensitivity per unit of power. For a power input of 19 mW, in-plane and out-of-plane sensitivities are 246 and 19 mK/g, respectively. The layout of the proposed accelerometer is then implemented together with its 3-axis readout circuitry.