The actin cytoskeleton is modulated by regulatory actin-binding proteins which fine-tune the dynamic properties of the actin polymer to regulate function. One such actin-binding protein is tropomyosin (Tpm), a highly-conserved alpha-helical dimer which stabilises actin and regulates interactions with other proteins. Temperature sensitive mutants of Tpm are invaluable tools in the study of actin filament dependent processes, critical to the viability of a cell. Here we investigated the molecular basis of the temperature sensitivity of fission yeast Tpm mutants which fail to undergo cytokinesis at the restrictive temperatures. Comparison of Contractile Actomyosin Ring (CAR) constriction as well as cell shape and size revealed the cdc8.110 or cdc8.27 mutant alleles displayed significant differences in their temperature sensitivity and impact upon actin dependent functions during the cell cycle. In vitro analysis revealed the mutant proteins displayed a different reduction in thermostability, and unexpectedly yield two discrete unfolding domains when acetylated on their amino-termini. Our findings demonstrate how subtle changes in structure (point mutations or acetylation) alter the stability not simply of discrete regions of this conserved cytoskeletal protein but of the whole molecule. This differentially impacts the stability and cellular organisation of this essential cytoskeletal protein.