Dear Paul,

hard to say, because absolute precipitation values defining arid conditions are difficult/impossible to reconstruct for mesozoic terrestrial ecosystems. And finding bones in deposits connected to desert environmental settings means they have died there, but living and surviving over a long time is hard to prove. Best indicator for answering your question might be trace fossils (tracks, nests, etc.).

There are some papers about dinosaur presence in aeolian and similar deposits (regarded as desert deposits) from Mongolia (Gradziński & Jerzykiewicz 1974; Fastovsky et al., 1997; Saneyoshi et al., 2011) and the US (Riese et al., 2011). The last paper reconstruct dinosaur presence in desert wetlands, which are important ecosystems in terms of (palaeo)biogeography through the geological history (Pigati et al., 2014).

Best regards

Johannes

Gradziński & Jerzykiewicz 1974 Dinosaur- and mammal-bearing aeolian and associated deposits of the Upper Cretaceous in the Gobi Desert (Mongolia). Sedimentary Geology 12(4): 249-278.

Fastovsky et al., 1997 The Paleoenvironments of Tugrikin-Shireh (Gobi Desert, Mongolia) and Aspects of the Taphonomy and Paleoecology of Protoceratops (Dinosauria: Ornithishichia). Palaios 12: 59-70.

Saneyoshi et al., 2011 Trace fossils on dinosaur bones from Upper Cretaceous eolian deposits in Mongolia: Taphonomic interpretation of paleoecosystems in ancient desert environments. Palaeogeography, Palaeoclimatology, Palaeoecology

 311: 38–47.

Riese et al., 2011 Synapsid Burrows and Associated Trace Fossils in the Lower Jurassic Navajo Sandstone, Southeastern Utah, U.S.A., Indicates a Diverse Community Living in a Wet Desert Ecosystem. Journal of Sedimentary Research

81: 299-321.

Pigati et al., 2014 Desert wetlands in the geologic record. Earth-Science Reviews 132: 67-81.

Dear Paul

As you know the dinosaurs were frequent during Tirassic to Cretaceous, the attached file is schematic diagram which allows the change in paleo temperature during Geologic time.  Currie and Padian (1997) have mentioned to distribution of dinosaurs which show development of their taxa.

link: https://books.google.com/books?id=7t9M5TsmjOUC&pg=PA572&lpg=PA572&dq=paleo+temperature+of+Dinosaurs+time&source=bl&ots=0GFlVa4VI2&sig=Q3my0emP0JseHtG2WzqXfXtARsk&hl=en&sa=X&ved=0CE0Q6AEwB2oVChMIpcTDzsfYxwIVR5QsCh2IQQQ9#v=onepage&q=paleo%20temperature%20of%20Dinosaurs%20time&f=false

An abrupt event 65 million years ago thought by many to be caused by the impact of a asteroid hitting near present day Yucatan, Mexico, has become known as the KT Boundary or Cretaceous-Tertiary mass extinction event, which caused cooling and perhaps other environmental factors that led to the extinction of 70% of the species and 40% of all genera living at the time, ending the age of the dinosaurs. (Alvarez, 1980). Moreover sea-level change is another proof which supports the paleotemperature in https://books.google.com/books?id=wVySAAAAQBAJ&pg=PA233&lpg=PA233&dq=paleo+temperature+of+Dinosaurs+time&source=bl&ots=ym10Ki7x_a&sig=C6_et34KXrmbMyUvEdb1y8-Pf8c&hl=en&sa=X&ved=0CEUQ6AEwBzgKahUKEwiSl5rzy9jHAhXCjSwKHXuEBic#v=onepage&q=paleo%20temperature%20of%20Dinosaurs%20time&f=false age (attachment 2). Eventually  Titus and Loewen (2013) reflected the lose of temperature in Late Cretaceous as case study.

link: https://books.google.com/books?id=wVySAAAAQBAJ&pg=PA233&lpg=PA233&dq=paleo+temperature+of+Dinosaurs+time&source=bl&ots=ym10Ki7x_a&sig=C6_et34KXrmbMyUvEdb1y8-Pf8c&hl=en&sa=X&ved=0CEUQ6AEwBzgKahUKEwiSl5rzy9jHAhXCjSwKHXuEBic#v=onepage&q=paleo%20temperature%20of%20Dinosaurs%20time&f=false

Additionally the dinosaurs adopted in warm climate which is confirmed by paleo atmospheric evidence such as concentration of CO2. and other physiological blood system.

Regards

Massih 

Dear Paul,

  In a recent publication (Tanner, Lawerence H., Galli, Kenneth G., and Lucas, Spencer, 2014, Pedogenic and lacustrine features of the Brushy Basin Member of the Upper Jurassic Morrison Formation in western Colorado: Reassessing the paleoclimatic interpretation, in: Tanner, L. . H., and Lucas, S., eds., Volumina Jurassica, special issue: The Jurassic of North America's Western Interior, Polish Geological Institute, Warsaw, Poland. Volumina Jurassica, 2014, XII (2): 115-130.) we present evidence within the Brushy Basin Member, Morrison Fm., western Colorado, that there is a clear difference in the types of paleosols between the Lower Brushy Basin and the Upper Brushy Basin rocks. Lower Brushy Basin sols are predominantly calcareous Aridisols that have Stage I - Stage III calcrete Bk horizons, abundant root traces, sometimes with vertic features, but only rarely with ochric epipedons. This is in contrast to the Upper Brushy Basin sols that are mostly thicker and usually have ochric epipedons and well-developed Bt and Bw horizons; we interpret them to be order Inceptisols.  

  Limestones within the Jmb are either homogeneous micrites or limestones with strongly brecciated textures. We interpret these as the deposits of carbonate in small water bodies on a low-gradient floodplain whose textures resulted from pedogenic reworking of the carbonate sediment.. We find no evidence for the presence of extensive lacustrine or wetlands (Lake T' oo' dichi') deposits anywhere in our study area that included the Trail Through Time, westernmost CO near UT border, the Fruita Paleontological Resource Area, and Echo Canyon, which is a side canyon of No Thoroughfare Canyon, south of Grand Junction, CO and near the eastern boundary of the Colorado National Monument.

 Paleoclimate was thus strongly seasonal but subject to variations on orbital (precessional and higher) timescales that caused periods of semi-aridity during weaker monsoons, to alternate with sub-humid periods during stronger monsoons. This apparent long-term change in climate during Brushy Basin deposition possibly was caused by the northward drift of North America. This may have caused the increase in humidity over the duration of Jmb deposition.

best, Ken