With device miniaturization comes the need to measure temperature changes on molecular scales. Recent experiments show that thermoresponsive devices may be constructed based on the temperature-dependence of the relative populations of left- and right-handed nucleic acid helical conformations: upon an increase in temperature, particular sequences of DNA oligonucleotide duplexes in high salt conditions switch from a left-handed (Z) form to a right-handed (B) one, while RNA responds inversely by switching from a right(A) to a left-handed (Z) form. We use existing temperature-dependent circular dichroism experimental data [Tashiro and Sugiyama, 2005] and a two-state model to extract the entropic contribution to the free energy difference between left- and right-handed form. Then, to address the microscopic origin of the inverse temperature response of RNA and DNA, we perform all-atom molecular dynamics simulations from which we compute both configurational nucleic acid and solvent entropies for a number of RNA and DNA systems; because the ionic conditions in the experiments are outside the physiological range, we cover a wider landscape of sequence, salt conditions, and helical direction. Calculations reveal a complex interplay between configurational, water, and ionic entropies, which, combined with the sequence-dependence, rationalize the experimentally observed transitions from A- to Z-RNA and Z- to B-DNA in high salt concentrations and provide insight that may aid future developments of the use of nucleic acids oligomers for thermal sensing at the nanoscale in physiological conditions.