  In this paper, we propose fitting unobserved component models to represent
the dynamic evolution of bivariate systems of centre and log-range temperatures
obtained monthly from minimum/maximum temperatures observed at a given
location. In doing so, the centre and log-range temperature are decomposed into
potentially stochastic trends, seasonal, and transitory components. Since our
model encompasses deterministic trends and seasonal components as limiting
cases, we contribute to the debate on whether stochastic or deterministic
components better represent the trend and seasonal components. The methodology
is implemented to centre and log-range temperature observed in four locations
in the Iberian Peninsula, namely, Barcelona, Coru\~{n}a, Madrid, and Seville.
We show that, at each location, the centre temperature can be represented by a
smooth integrated random walk with time-varying slope, while a stochastic level
better represents the log-range. We also show that centre and log-range
temperature are unrelated. The methodology is then extended to simultaneously
model centre and log-range temperature observed at several locations in the
Iberian Peninsula. We fit a multi-level dynamic factor model to extract
potential commonalities among centre (log-range) temperature while also
allowing for heterogeneity in different areas in the Iberian Peninsula. We show
that, although the commonality in trends of average temperature is
considerable, the regional components are also relevant.
