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Sadie, to Aquaria Central, home to the most golden fish keepers on the internet !!!
What kind of tetras do you have?
What do you mean by "fancy GF"? If you mean the standard fantails, veiltails or moors, then the water temp would be fine. As for the bubble eyes, pearlscales, lionheads, and the deeper-bodied ryukins, the water temp should be warmer than 72 degrees, more in the range that PBQ recommended.
<<Digression, here>>From a perverse standpoint, I'd be interested in seeing if the GF did eat the tetras. The standard thought is that GF and tropicals don't mix well, so I've never seen them together. I do have some very aggressive feeders, though. This subject is a little close to home because to me because I had a 55g tank that was going to house a cardinal tetras and keyhole cichlids (I'd read that keyholes were peaceable cichlids) but when the tetras were introduced, the keyholes had eaten two within minutes. I was crushed. So now I'm always looking at "peaceful" fish a little differently.
Val