Re: How hot must a nuclear reactor get before it begins to meltdown?

The temperature at which a meltdown occurs is the melting point of the fuel used. Different types of reactors will use different types of fuels, so the answer to your question is yes. For example, the melting point of stochiometric uranium oxide, UO₂, is 2865.

Mixtures of uranium and plutonium, such as would exist in "mixed oxide" (MOX) fuels, will melt at slightly lower temperatures and non-stochiometric uranium oxides melt at slightly lower temperatures than 2865

Other types of fuels such as metal alloy fuels used in some research reactors and ceramic pellets used in high temperature gas cooled reactors have different melting points than the oxide fuels mentioned above.

Reference: "Fundamental Aspects of Nuclear Reactor Fuel Elements" TID-26711-P1, US Department of Energy, 1976