From experience with several sets of fog lights on my wife's 2011 Ford Escape (the same housings used on 2010 - 2013 Camaros, 2007 - 2013 Avalanches, 2007 - 2014 Suburbans, as well as several other vehicles), I can assure you that LED bulbs — even the 4,000-lumen versions — will not melt your plastic fog light lenses at all.
Your fog light housings are roughly the same dimensions as the versions on my wife's SUV.
The LEDs are cooled by fans that do such a good job, the plastic lens only gets very mildly warm to the touch.
However, HIDs — both 35-watt and, especially, 55-watt — will certainly cause your reflector to melt around the bulb, and will cause a large heat dimple above the bulb on the lens cover.
Additionally, the lens will get so hot, you will burn your hand and even in the cold temperatures of wintertime, and the plastic lenses will melt even while driving in rain or at freeway speeds; rainwater and high-speed airflow aren't even enough to cool them down.
I was skeptical about LED headlight bulbs and fog light bulbs, but once I tried them, there's no way that I'll go back to HIDs again. As long as you get versions that put out at least 3,000- to 4,000-lumens each, (and not the decorative ones that are inexpensive and are generally listed as "fog light and DRL use only), you'll enjoy crisp, clear light that won't blind other drivers and is a nice improvement over the quality of HID.
I've found that, with round reflectors, LEDs bulbs with diodes closest to the housing reflector put out the best quality of light.
As a final example, I originally ran HIDs in our 1999 Mercury Tracer wagon. The light output was somewhat scattered and created distracting pools of light in front of the car. When I switched to LEDs, the light was brighter — but non-blinding to on-coming traffic — and was evenly distributed across the road. My LED bulbs were approximately $50.00 for the pair, and have been one of the very best upgrades that I've made to any of my three vehicles.
Use your best judgement to determine what will work best for you and your specific application.
Have a blessed day!