One of the gang, an Asian man, entered the common prayer room 30 minutes before the robbery took place.
Once there, he watched members of the temple on St Andrew's Drive in the city's South Side counting up the proceedings from a fundraising walk held earlier in the month to celebrate the festival of Vaisakhi.
It is understood the man then used a mobile phone to contact two other members of the gang who entered the temple, brandished a firearm, and demanded the money.
The undercover worshipper then slipped his shoes back on and left the temple with the other members of the gang.
The incident happened at about 11:20am on Sunday, as members of the temple were preparing for the day's services.
The Sikh faith allows any of its faithful to attend a temple prayer room as long as they observe the rituals of washing their hands, taking off their shoes and covering their heads with a cloth.
Kalwanti Singh, a member of the congregation, and former vice-president of the temple, said the Asian member of the gang did not reveal himself until the robbery was almost over.
He said: "The Asian chap was posing as a member of the congregation, but he sat in an area out of view of the CCTV, so it could be that he used his mobile to contact the two other guys to say, 'go for it, now's the time', because he had been sitting there for 30 minutes.
"They (the other men] came in very quietly – one guy covered his head, the other was wearing a baseball cap – and they just marched up the stairs and literally seconds later they marched out again with the money.
"The people in the kitchen didn't even know what had happened. The people sitting up in the prayer room were just amazed at what had happened. It really is shocking."
The firearm was not used during the robbery and no-one was injured, but worshippers who had witnessed it, including women and children, were said to be shaken by what happened.
It is understood that CCTV cameras posted both in and outside the building had caught images of all three men and that Strathclyde Police were now examining them.
Mr Singh said the temple members felt that it had been defiled by the robbery. "We're shocked, it is a sacred place of worship and it feels violated. We've never been in this position before, it's a very good neighbourhood around here."
He added that though until now it had been very much a walk-in centre, they would now be reviewing security.
Strathclyde Police yesterday issued descriptions of the three men. The first is described as a black male, about 6ft, with a slim build and short dark hair.
The second is described as a black male, in his mid-twenties, about 6ft tall, with a slim build. The third is an Asian male, in his early twenties, 5ft 3in to 5ft 5in tall, with a stocky build.