I held gallium under a heat lamp. It didn't melt. I didn't even find a thin film of liquid gallium. Can anyone explain why? Does gallium rust?
Having recently had an opportunity to play around with some gallium of my own, I have a few thoughts.
It's possible you have a different metal than what you thought you had, but frankly, I don't think that's very likely.
It takes a surprising amount of absorbed heat to melt gallium. Putting a sizable chunk of gallium in $35~^\circ\mathrm C$ water doesn't cause it to melt immediately. Even boiling water doesn't melt it instantly. Because gallium is a metal, it conducts heat fairly well, so when heated gently, it won't melt until the temperature of the whole piece gets close to the melting point.
As mentioned by user5134, a shiny metal like gallium isn't going to pick up heat very quickly from a radiative source like a heat lamp. If you wait long enough, it'll definitely melt. If you want to melt the gallium relatively quickly, then you'll want to put it into physical contact with something warm. The standard method for melting solid gallium in a container is to just immerse the closed container in hot water (not boiling water, especially if the container is glass).
Gallium metal may be obtained in the elemental form. A classic demonstration is to hold gallium in your hand and watch it melt.
The energy from the heat lamp must be absorbed by the gallium, but if the IR light is reflected, then it may not be getting hot enough to melt.
It's also possible that you have an alloy of gallium and some other metal and that the melting point is higher than for pure gallium.
Maybe it is another metal.
If you are sure it is gallium try melting it with your hand, smaller pieces melt faster.
Gallium oxide layer is too small to make a difference, it takes hundreds of years for it to completely rust.
It is very important to note that storing it in a metal container will ruin your sample and that storing the gallium while it is a liquid in a glass container is dangerous because it expands when solidifying.
You can also measure gallium' density around 6 g/cm3 with a water cup placing the gallium and seeing how much volume it increased and weighting it (remember that gallium amalgamates metals so measure them with not metal tools.
Divide the weight in grams with the volume and you should get a number lower than 6 and higher than 5.7.