With the continuous increasing demands of high performance processors in Machine Learning (ML) and high performance computing (HPC) market segment, the CPU power dissipation is dramatically growing due to the increasing core count/frequency, the complexity of MCP(multi-chip package) structure and etc. The Thermal Design Power (TDP) of Intel Xeon and Intel Xeon Phi Processor is increasing from generation by generation. As a result, the adoption of the advanced cooling technology, such as liquid cooling solution, is considered which can provide better cooling capability compared with traditional air cooling in engineering application. This paper introduces a unique thermal analysis and design methodology for liquid cooling solution which can be used for Liquid Assisted Air Cooling (LAAC) and also for rack liquid cooling systems. In the paper, the detailed design parameters including the thermal resistance network of liquid cooling, the performance curve of pump, air/liquid to liquid heat exchanger (HEX) and liquid temperature limitations are discussed to frame the design methodology. Finally, a case study with simulation and thermal test data are presented to demonstrate the accuracy of the methodology proposed in this paper with a half width 1U form factor server system.