“The concept of one considering to enter a makom kedusha without a hat and jacket, is a difficult one to contemplate.”
“Really a Yid should wear a hat and jacket anywhere he goes.”
If you wear your hat and jacket everywhere you go, then it goes without saying you should wear it into a makon kadosh. the question is, how is your hat and jacket anything special for davening or do you have a special davening jacket? do you put on a tie? Do you wear your hat with brim up in the street and down by davening?