The Maharshal, who was a cousin and student of the Rema, sent him a scathing letter in which he criticized him for utilizing an opinion of Aristotle. The Rema responded with this interesting responsum concerning the permissibility of studying Greek philosophy/wisdom. In the responsum he protests that he had never studied Aristotle directly and only what was known to him through the Moreh Nebhukhim and Sha'ar ha-Shamayim, as you quote from Y.D. Shulman above.
R. Yaaqov Shelomo Topolinsky in his work Imrei Sefer (p. 474) ties it to the שער השמים of R. Gershon b. Shelomo, as DoubleAA surmised in the comments.
R. Gershon b. Shelomo lived in the 13th century and is most often cited as having been from Catalonia (others suggest Languedoc or Provence). The Sefer Yuhsin and Seder ha-Doroth claims that this R. Gershon was in fact the father of the Ralbag (R. Lewi b. Gershon, aka Gersonides) and was the son-in-law of Nahmanides. Others have found this claim to be doubtful as the Ralbag makes no mention of this book nor of Nahmanides (A Study of Gersonides in His Proper Perspective, p. 26). For a contemporary account of the extant scholarship on the topic see James T. Robinson's "Gershom Ben Solomon's Sha'ar Ha-Shamayim: Its Sources and Use of Sources" (chapter 11 of The Medieval Hebrew Encyclopedias of Science and Philosophy).