The modeling of Micro- and NanoElectroMechanical Systems (MEMS and NEMS) requires new computational techniques that can deal efficiently with geometric complexity and scale dependent effects that may arise. Reduced feature sizes increase the coupling of physical phenomena and noncontinuum behavior, often requiring models based on molecular descriptions and/or first principles. Furthermore, noncontinuum effects are often localized to small regions of (relatively) large systemsprecluding the global application of microscale models due to computational expense. Multiscale modeling couples efficient continuum solvers with detailed microscale models to providing accurate and efficient models of complete systems. This thesis presents the development of multiscale modeling techniques for nonequilibrium microscale gas phase phenomena, especially thermally driven microflows. Much of this focuses on improving the ability of the Information Preserving DSMC (IP-DSMC) to model thermally driven flows. The IP-DSMC is a recent technique that seeks to accelerate the solution of direct simulation Monte Carlo (DSMC) simulations by preserving and transporting certain macroscopic quantities within each simulation molecules. The primary contribution of this work is the development of the Octant Splitting IP-DSMC (OSIP-DSMC) which recovers previously unavailable information from the preserved quantities and the microscopic velocities. The OSIP-DSMC can efficiently simulate flow fields induced by nonequilibrium systems, including phenomena such as thermal transpiration. The OSIP-DSMC provides an efficient method to explore rarefied gas transport phenomena which may lead to a greater understanding of these phenomena and new concepts for how these may be utilized in practical engineering systems. Multiscale modeling is demonstrated utilizing the OSIP-DSMC and a 2D BEM solver for the continuum (heat transfer) model coupled with a modified Alternating Schwarz coupling scheme. An interesting application for this modeling technique is Thermal Sensing Atomic Force Microscopy (TSAFM). TSAFM relies on gas phase heat transfer between heated cantilever probes and the scanned surface to determine the scan height, and thus the surface topography. Accurate models of the heat transfer phenomena are required to correctly interpret scan data. This thesis presents results demonstrating the effect of subcontinuum heat transfer on TSAFM operation and explores the mechanical effects of the Knudsen Force on the heated cantilevers.