To my knowledge there has never been a house of worship on that street. I think TEMPLE was somebody's last name.
Note that the block parallel to Temple Ave (alias Cork Street), northwards, is called Emerald Place, or Emerald Street. Definately a connection with Ireland regarding these street names. The area is believed to have been majority-Irish back when most of the houses were built, early 1900's. It was known as a blue-collar, working-class neighborhood, with many local residents working in the wallpaper factory that later became Packards.
Around the 1920's, the part of the Fairmount Community west of Main Street also had some Irish, but may have been as much as 80% or 90% white-Protestant population. A great many persons of English, Scottish, Dutch, German, and Scandinavian ancestry (or some combination thereof) lived west of Main Street all the way to the Maywood and Paramus borders. This concentration slowly diminished with the arrival of more Irish. At some point the Irish were considered to be part of the majority population, unsure when that happened, but it was way before my time. But at no point was the neighborhood over half Irish. Not even on Willow and Catalpa Avenues where there were the most Irish.
The same pattern repeated with Italians, who only started coming to the Fairmount section after World War II. By the 1960's the influx was strong, and by the late 1970's, most of the houses selling went to Italian families. There was sort of an Italian "high tide" that came in, peaked, and began diminishing by 1990. There was also a much lesser influx of Jewish families after WWII, but for the most part it was only on or within one block of Summit Avenue.
I grew up in the Fairmount Section in the 1970's, and even then there were quite a few older residents who resented what they called an "invasion" of Italian families. I can remember neighbors gossiping about it to my parents, who didn't consider it to be an enormous problem, because all of us were white. Looking back, the whole matter seems even more absurd.