Not sure if here or physics is the best place for this question, but if there was a meteor that had gold in it, what happens to that metal during entry of the Earth's atmosphere? Since gold melts at 1948° F (1046°C) and boils at 5378° F (2970°C), and Space.com says a meteor reaches about 3000° F (1650 °C) on average, even if that's just the surface temp, some gold would liquify (I think). I'm guessing depending on the angle of entry, it could retain enough velocity to leave the atmosphere, but I think at least it some cases, it could rain down as either liquid or solid gold and would be gold meteorites.
As it melted, it would be broken up into a spray or even a mist by the airstream. The droplets would quickly slow down to their terminal velocity and solidify, so you would get a fine gold dust imperceptibly falling over a wide area.
I am basing this on my admittedly incomplete understanding of meteors that do not contain gold. When the one in Russia some years ago exploded, it didn't vaporize, but only so many pieces were found.
Would a gold-containing meteor cause it to “rain” gold?
First, it is a bit unclear what do you mean by "gold-containing meteor". All solar system bodies have gold, the question is how much. For this answer I will assume that you mean a meteorite with chunks of visible gold nuggets in it, nothing that this is a hypothetical concept as no such meteorites are known or expected.
Meteors, when in space, are very very very very cold. Their travel duration in Earth's atmosphere is very short, just a couple of seconds. Actual melting only occurs at the very most outer layer of the meteorite. This is not sufficient to heat up the interior of the meteorite to any significant degree. In fact, some meteorite falls have found to have frost on them when found soon after landing, because they condense the moisture in the air around them! Some meteorites still contain organic material which would be destroyed at much lower temperature than the melting point of gold.