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We aim to study the excitation conditions of the molecular gas in therotating disk of the Red Rectangle, the only post-Asymptotic-Giant-Branchobject in which the existence of an equatorial rotating disk has beendemonstrated. For this purpose, we developed a complex numerical code thataccurately treats radiative transfer in 2-D, adapted to the study of molecularlines from rotating disks.  We present far-infrared Herschel/HIFI observations of the 12CO and 13COJ=6-5, J=10-9, and J=16-15 transitions in the Red Rectangle. We also presentour code in detail and discuss the accuracy of its predictions, from comparisonwith well-tested codes. Theoretical line profiles are compared with theempirical data to deduce the physical conditions in the disk by means of modelfitting.  We conclude that our code is very efficient and produces reliable results.The comparison of the theoretical predictions with our observations revealsthat the temperature of the Red Rectangle disk is typically ~ 100-150 K, abouttwice as high as previously deduced from mm-wave observations of lower-J lines.We discuss the relevance of these new temperature estimates for understandingthe thermodynamics and dynamics of this prototype object, as well as forinterpreting observations of other rarely studied post-AGB disks. Despite oursophisticated treatment of the line formation, our model cannot explain therelatively strong line-wing emission for intermediate-J transitions. We arguethat a model including a rotating disk only cannot reproduce these data andsuggest that there is an additional extended (probably bipolar) structureexpanding at about 7--15 km/s.

Warm gas in the rotating disk of the Red Rectangle: accurate models of molecular line emission