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Peter Thanks for the question.
It's possible that a record of Bloem's visit exists somewhere. However a the papers of Calvin Coolidge and their history highlight the importance of what Franklin Roosevelt would later do in establishing a Presidential library for the American people.
Coolidge was well known for his privacy and reserve. According to the provenance note on the Index for the Calvin Coolidge Papers at the Library of Congress, Coolidge had no intention of saving his personal papers. Grace Coolidge wrote in 1953 that her husband had destroyed all of his "personal" papers. Much of what we might know or discover about his administration, or his opinion on issues of domestic and foreign policy, was lost.
Coolidge did give some of his papers to the Forbes Library in Northampton, MA. These papers relate to when he was Massachusetts governor and Vice President. There are some correspondence files from his time as President as well. Perhaps they might have some information related to Walter Bloem. Calvin Coolidge Presidential Library and Museum | Forbes Library
The Calvin Coolidge Papers at the Library of Congress, the larger collection of Coolidge papers, are primarily correspondence files left at the White House after the end of the administration. There is a fairly comprehensive index of names. A link to the collection can be found here: https://lccn.loc.gov/mm79016741
Since Coolidge destroyed so many of his papers it might also be worth while examining the papers of Edward T. Clarke, also at the Library of Congress, who was Coolidge's personal secretary for a number of years.
Questions about the Coolidge Papers and other materials at the Library of Congress can be asked here Manuscript Reading Room - Ask a Librarian (Library of Congress)