Complementary Metal Oxide Semiconductor (CMOS) has always remained the dominant integrated circuit technology specifically for designing digital circuits. This paper examines the modelling (utilizing $\alpha$-power based MOSFET model), simulation (utilizing HSPICE simulation) and optimization (utilizing Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) techniques) of ultradeep submicron CMOS based digital inverter, performs insightful analysis and extracts formulas for the optimal transistor sizing. Additionally, the study serves as an implementation forum for the thermal analysis of transient characteristics of CMOS inverters at the ultradeep submicron technology node (at 300K and 400K). The results lie within the acceptable range of 1-10\%.