Bioinks are usually cell-laden hydrogels widely studied in bioprinting performing experimental tests to tune their rheological properties, thus increasing research time and development costs. Computational Fluids Dynamics (CFD) is a powerful tool that can minimize iterations and costs simulating the material behavior using parametric changes in rheological properties under testing. Additionally, most bioinks have specific functionalities and their properties might widely change with temperature. Therefore, commercial bioinks are an excellent way to standardize bioprinting process, but they are not analyzed in detail. Therefore, the objective of this work is to study how three temperatures of the Cellink Bioink influence shear stress pressure and velocity through computational simulation. A comparison of three conical nozzles (20, 22, and 25G) for each temperature has been performed. The results show that shear stress, pressure, and velocity vary in negligible ranges for all combinations. Although these ranges are small and define a good thermo-responsive bioink, they do not generate a filament on the air and make drops during extrusion. In conclusion, this bioink provides a very stable behavior with low shear stress, but other bioprinting parameters must be set up to get a stable filament width.