The statistical properties of temperature maxima are investigated in a very long integration (2 400 000 months) of an intermediate order Quasi-Geostrophic model displaying deterministic chaos. The variations of the moments of the extreme value distributions as a function of the time window, n, are first explored and compared with the behaviours expected from the classical Generalized Extreme Value (GEV) theory. The analysis reveals a very slow convergence (if any) toward the asymptotic GEV distributions. This highlights the difficulty in assessing the parameters of the GEV distribution in the context of deterministic chaotic (bounded) atmospheric flows. The properties of bivariate extremes located at different sites are then explored, with emphasis on their spatial dependences. Several measures are used indicating: (i) a complex dependence of the covariance between the extremes as a function of the time window; (ii) the presence of spatial (non-trivial) teleconnections for low-amplitude extremes and (iii) the progressive decrease of the spatial dependence as a function of the amplitude of the maxima. An interpretation of these different characteristics in terms of the internal dynamics of the model is advanced.