Monolithic 3D (M3D) integration reduces the wire length, which eventually improves energy efficiency and performance compared to 2D integration. However, 3D integration inevitably causes higher on-chip temperature compared to 2D integration due to the increased power density as well as worse heat dissipation. The high on-chip temperature may offset the benefits of the M3D microprocessors due to the following reasons: 1) high on-chip temperature increases leakage power, which degrades energy efficiency. 2) the actual clock frequency is limited at run-time by frequent dynamic thermal management (DTM) invocations. In this paper, for the first time, we explore the thermal feasibility (whether it is possible to achieve high energy efficiency and performance without exceeding threshold temperature) of the M3D microprocessors depending on cooling solutions. For the thermal feasibility study, we construct an integrated framework to investigate the thermal behaviors and thermal feasibility of different types of microprocessors (M3D, 2D, and through-silicon-via based 3D (TSV-3D)) with different cooling solutions. Our thermal-aware evaluation results show that the best configuration of the M3D microprocessors reduces average energy consumption by 27.6% compared to the 2D microprocessor at an iso-frequency (4.0GHz). In addition, at the highest clock frequencies satisfying both design and thermal constraints, the best configuration of the M3D microprocessors improves average system performance by 25.1% and 26.0% compared to the 2D and TSV-3D microprocessors, respectively.