First, thank-you Dave for the kind words.
Just so we're on the same page terminology-wise, the rear deck lid's primary lifting mechanism are a pair of hydraulic cylinders; they are assisted by a pair small gas struts partially hidden by the rat fur on the side of the trunk. The reported failure rates for the gas struts are low, but like anything else, they aren't immune to failure. Make sure your Folding Top hydraulic fluid level in the reservoir on top of the pump is between the min/max marks.
There are a few other things you can do before you start buying parts. The first question I have is in relation to the symptoms you describe. You said the top is failing when it's hot. Does it operate nominally when it's cool? There is a thermistor located on the inside/bottom of the Folding Top hydraulic motor that will inhibit motor operation if it's too hot or cold. It should flag a message on your DIC to report this.
With a couple of beers and a trusted helper, have them press the Folding Top Control switch while you gently pull upwards on the rear deck lid. If a strut, (or a hydraulic cylinder) have failed, this should enable the pump to raise the deck lid, and you can verify the pump's operation. If the Rear Deck lid raises, but settles back down when you let go of it, either hydraulic fluid is leaking by a cylinder seal, or the gas strut(s) aren't doing their job.
If the Rear Deck lid unlatches, but nothing happens, your pump may have failed. Usually, (and it certainly happened to me) if the pump is failing, it will partially move the top but stop at some point when it can't supply enough pressure. It's an expensive repair, and a worst-case scenario, to be sure. Listen for it to try to operate; at least you know it's getting a command to run. Another item that can fail and cause the Rear Deck lid to not move is a Solenoid valve in the hydraulic manifold which supplies hydraulic oil to the lift cylinders. These can be individually operated and verified with a Tech 2.
If the gas strut(s) have indeed failed, this would be the cheapest repair and something you could replace. Gather some more symptoms, and if you need to replace them, I can write up a procedure. I'll hit the books later and see if there's a documented checkout for them. Since they can be removed easily enough, you could support the Rear Deck lid with a 2x4, pull them off and compare each by compressing them.
CC