Temperament is an important trait for the management and welfare of animals and for reducing accidents involving people who work with cattle. The present study aimed to estimate the genetic parameters related to the temperament score (T) and weaning weight (WW) of Nellore cattle, reared in a beef cattle breeding program in Brazil. Data were analyzed using two different two-trait statistical models, both considering WW and T: (1) a linear-linear model in which variance components (VCs) were estimated using restricted maximum likelihood; and (2) a linear-threshold model in which VCs were estimated via Bayesian inference. WW was included in the analyses of T to minimize any possible effects of sequential selection and to allow for estimation of the genetic correlation between these two traits. The heritability estimates for T were 0.21±0.003 (model 1) and 0.26 (model 2, with a 95% credibility interval (95% CI) of 0.21 to 0.32). The estimated genetic correlations between WW and T were of a moderate magnitude (−0.33±0.01 (model 1) and −0.34 (95% CI: −0.40, −0.28, model 2). The genetic correlations between the estimated breeding values (EBVs) obtained for the animals based on the two models were high (>0.92). The use of different models had little influence on the classification of animals based on EBVs or the accuracy of the EBVs.