Enzymes are eco-friendly and natural molecules with excellent properties. It is highly desirable to rationally engineer enzymes for target application in pharmaceutical, textile, and food industries. However, there are no clear design principles that enable this using rational site-directed mutagenesis approaches. In this work, molecular dynamics simulations were used to probe the activity–temperature relation used to explain the tradeoff between activity and stability in thermophilic and psychrophilic enzymes. Specifically, it was investigated whether the conventional idea that higher active site flexibility leads to activity at low temperature in psychrophilic enzymes can be used as a design principle to incorporate low temperature activity in a thermophilic enzyme for engineering broad range temperature active enzymes. These results indicate that simple design rules like reducing hydrogen bonding residues near the active site do not allow for changing active site flexibility in isolation and lead to changes in flexibility in the entire enzyme. Consequently, undesirable functional and specificity changes in the enzyme are observed. It was demonstrated that studying residue–residue flexibility correlations can address this challenge and provide appropriate design guidelines to rationally engineer the active site flexibility. Such correlations can be valuable in minimizing false positives in high-throughput screening methods based on directed evolution and/or machine learning-based engineering of enzyme activity-temperature relation.