'Medieval science' may seem an oxymorom. What did monks and shepherds know about science? In fact there was a great deal of natural inquiry in Medieval Europe, done by philosophers and anatomists and princes as well as by monks and shepherds. But this inquiry was usually radically different from our own conception of natural science. The challenge for the historian is to understand Medieval natural knowledge on its own terms.
Read the general survey by Shank. Then choose one of the specific topics, either Aquinas or the Physiologus. Read the primary text first (the Summa or the Physiologus). This text will probably strike you as strange and wrong-headed. Make a note of the things that give you this impression, whether they are terms, concepts, literary forms, modes of argument, or whatever. Then read the corresponding secondary text (by Aertsen or Harrison). This should help you understand the context in which the primary text was written. Now go back to the primary text, reading it again with the context in mind. Does it make more sense?
Shank, M. 'Myth 1. That There Was No Scientific Activity between Greek Antiquity and the Scientific Revolution', in Ronald Numbers and Kostas Kampourakis, Newton's Apple and Other Myths About Science (Harvard UP, 2015)
St Thomas Aquinas, Summa Theologiae, Question 57, articles 1 (Whether it was fitting for Christ to ascend to heaven?) and 4 (Did He ascend above all the corporeal heavens?). Available online here.
Jan A. Aertsen, 'Aquinas' Philosophy in its Historical Setting', in Norman Kretzman and Eleonore Stump, eds., The Cambridge Companion to Aquinas (Cambridge UP, 1993) - Warwick ebook
Bishop Theobald, Physiologus: A Metrical Bestiary Of Twelve Chapters, trans. Alan Wood Rendell
(London: John & Edward Bumpus, Ltd., 1928), available online here - choose two animals from the contents list on page 4, and read the chapters on those animals.
'Worlds Visible and Invisible' (read up to page 27), Peter Harrison, The Bible, Protestantism, and the Rise of Natural Science (Cambridge UP, 1998), Warwick ebook
CHS2 - there are good chapters here to suit all tastes
Lindberg, David C., The Beginnings of Western Science, 2nd edition, chapters 9-13
Weisheipl, James A, ‘The Nature, Scope and Classification of the Sciences’, in Science in the Middle Ages, ed. by David C. Lindberg, Chicago History of Science and Medicine (Chicago: University of Chicago Press, 1978)