The Bayesian paradigm is becoming an increasingly popular framework for estimation and uncertainty quantification of unknown parameters in geo-physical inversion problems. Badlands is a basin and landscape evolution forward model for simulating topography evolution at a large range of spatial and time scales. Our previous work presented Bayeslands that used the Bayesian paradigm to make inference for unknown parameters in the Badlands model using Markov chain Monte Carlo (MCMC) sampling. Bayeslands faced challenges in convergence due to multi-modal posterior distributions in the selected parameters of Badlands. Parallel tempering is an advanced MCMC method suited for irregular and multi-modal posterior distributions. In this paper, we extend Bayeslands using parallel tempering (PT-Bayeslands) with high performance computing to address previous limitations in parameter space exploration in the context of the computationally expensive Badlands model. Our results show that PT-Bayeslands not only reduces the computation time, but also provides an improvement of the sampling for multi-modal posterior distributions. This provides an improvement over Bayeslands which used single chain MCMC that face difficulties in convergence and can lead to misleading inference. This motivates its usage in large-scale basin and landscape evolution models.