If the LED is burning out after just 10 seconds, it is not a heat issue. The aluminum star has enough heat capacity that it would take more than 10 seconds for it to overheat.
The XLamp should be able to handle 700mA, if it cannot, I suspect there is something wrong with your power supply.
One big thing you may be overlooking is that your "constant current" power supply may only be able to drop the voltage down to a limited level. This may or may not actually be indicated on the labeling. In other words, it is only constant current within a certain voltage range. The solution to your problem is that you are going to have to run multiple LEDs at the same time in a series circuit.
With one of the cheap Chinese-made constant current power supplies, I have to run at least four LEDs in series or they will burn out. And even then, they still burn out if I plug the power supply into an outlet while the LEDs are still attached, there is obviously a power surge that they cannot handle. All this despite the fact that the LEDs are rated to handle 700mA and it is only a "350mA" rated power supply! But there are no problems when using six or more LEDs.
If the power supply states 600mA 12-48v, that means you will have to use at least 4 LEDs in series (if each LED is rated 3 volts), otherwise the current will be greater than 600mA, and chances are one or more of the LEDs will burn out. Some LED power supplies will explicitly state they are for a string of 20-30 LEDs. That means if you only use 18 LEDs there will be a burn out. Because the power supply cannot lower its voltage below a certain threshold, and therefore the current (mA) will be greater than intended.
This, I suspect, is most likely your problem.
Again, just to clarify, what matters is the amount of current going through an LED. Generally an LED can take any level of voltage so long as the current is limited. However, voltage is nevertheless still an important consideration when using power supplies. This is because a constant current power supply controls the current going through the LEDs by changing the voltage. The LEDs act as resistors, so the higher the voltage, the more current is able to flow through. If the power supply is not able to drop its voltage below a certain threshold, the current passing through the LED will be greater than what the constant current power supply is rated for. In other words, with most "constant current" power supplies the current is not actually limited at the source, rather it is a feedback loop active modulation through the circuit.
The reason it is the current passing through an LED that matters is because wattage is determined by current and resistance, so too much current means too much power/heat. Theoretically, there could be a thousand volts going through the LED, but the LED itself would only pick up a small fraction of the overall power travelling through it, so could do just fine. This is the phenomena of voltage drop / power drop. If the load in the circuit only absorbs a fraction of the voltage, it will only pick up a fraction of the power.
