I recently purchased LEDs on ebay that were supposed to come attached to star PCB (as a heat sink). The items I received are just the LEDs (no PCB). They are listed as 3W LEDs, with a forward voltage of 3.0-3.4V, and current at 700mA.
I received a partial refund. Will I damage / destroy the LEDs if I use them without a heat sink? If not, what is the best way to mount these to preserve their life during operation?
If you received actual 3 W LEDs and were to run them at 3.5 V, 700 mA without a heatsink, then yes, you will sooner-rather-than-later kill them.
You have three options.
Related: What is the purpose of star pcb?
At the very least, running them without a heat sink would degrade their operating life. You can buy cheap bare star PCBs off of eBay. Most are from China, but I see at least one set in the U.S. Soldering might be difficult unless you have a reflow oven or hot air station. You could try using a thermal paste, but I doubt it would conduct heat as well as solder.
If you design your own PCB, you can add a thermal pad connected to a ground plane. That won't work as well as a star PCB since star PCBs have an aluminum substrate.
If you don't care about light output, you could try reducing the current and using no heat sink. Start at 25mA and monitor the temperature of the thermal pad with an IR thermometer. The LED datasheet should give a maximum operating temperature for the rated lifetime.
