During the past several decades, significant performance improvement of microprocessor chips has been obtained mainly by reduction of (transistor) device length scale. Beyond the International Technology Roadmap for Semiconductors (ITRS)-defined 50 nm technology node, the parasitic effects associated with reduction of the feature size (e.g., increase in leakage current) begin to outweigh the favorable effects of increased functionality and speed. One promising route for continued performance improvement is to exploit low temperature operation of microprocessors (also referred to as the temperature scaling [1]). This calls for development of compact, inexpensive, and quiet refrigeration/cryogenics technology, which can be interfaced with electronic components. In this work, we consider thermally driven sorption-assisted refrigeration technology for sub-ambient cooling of high performance electronics. In the past, sorption-based cryocoolers have been successfully developed for cryogenic cooling of sensors in space applications, targeting very low (mW-level) cooling loads. These cryocoolers are quiet, vibration free, reliable since they have no moving parts at high pressure, and therefore offer significant advantages over mechanical refrigeration. In addition, there is no refrigerant-lubricant interaction in sorption-based cryocoolers, which can potentially degrade the evaporator performance. This paper presents a thermodynainics-based analytical framework for the design of sorption compressors for cryogenic cooling of electronics. A sample case study is also presented to illustrate the approach.