We present the theory of thermal equivalence in the framework of the Peyrard-Bishop model and some of its anharmonic variants. The thermal equivalence gives rise to a melting index τ which maps closely the experimental DNA melting temperatures for short DNA sequences. We show that the efficient calculation of the melting index can be used to analyse the parameters of the Peyrard-Bishop model and propose an improved set of Morse potential parameters. With this new set we are able to calculate some of the experimental melting temperatures to ± 1.2 °C. We review some of the concepts of sequencing probe design and show how to use the melting index to explore the possibilities of gene coverage by tuning the model parameters.