  Climate change is commonly associated with an overall increase in mean
temperature in a defined past time period. Many studies consider temperature
trends at the global scale, but the literature is lacking in in-depth analysis
of the temperature trends across Australia in recent decades. In addition to
heterogeneity in mean and median values, daily Australia temperature data
suffers from quasi-periodic heterogeneity in variance. However, this issue has
barely been overlooked in climate research. A contribution of this article is
that we propose a joint model of quantile regression and variability. By
accounting appropriately for the heterogeneity in these types of data, our
analysis reveals that daily maximum temperature is warming by 0.21 Celsius per
decade and daily minimum temperature by 0.13 Celsius per decade. However, our
modeling also shows nuanced patterns of climate change depends on location,
season, and the percentiles of the temperature series over Australia.
