First thing to say is that I am definitely not the world expert on this. But I have struggled with the concept of the best way to warm up for the last few seasons and have seen first hand many of the worlds leading climbers doing their various routines. Learning from that, this is what I do now.
I get my heart rate up by cycling to the climbing wall. But this could be just a quick run before you start climbing. Nothing too prolonged and arduous but enough to get the heart rate up high for a several minutes, infact maybe as long as 20min. Then I try and loosen up. I'm not a huge advocate of static stretching although a bit of this might be necessary. I prefer to spend more time doing dynamic warming up, like circling my arms, wrists, ankles and shoulders, loosening up my hips and back from side to side. Some folks think 'windmilling' you arms and shoulders is bad. However I've watched Markus Bendler (world champion) do it everytime before a big comp. And he is pretty much the ultimate althlete in terms of mixed ice climbing, so I think I'd follow him rather than the doubters. Some static stretches for your arms, back and legs are good to do, but essentially drytool training is a very dynamic beast and static stretches just aren't enough. That said I do stretch my calves, hamstrings, triceps, biceps and back.
So now that my core is warmed up and my joints and limbs are looser, I warm up my hands and forearms. When all is said and done, they are the ones getting most hammered. I normally use spongey hand exercisers and a Powerball for several minutes. After this your hands, wrists and forearms should feel sufficiently woken up, maybe even with some minor pump. Another area that gets very stressed with any dynamic training is the elbow. Hence I always try to do at least 50 press-ups and 30 dips before I start training. The dips can be given various types of assistance in order to make them less strenuous as a warm-up.
Kat demonstrating a basic hand exerciser.
Then it's time to get going, but with the first few exercises being just easy traversing to help get the muscle-memory and brain-focus both tuned in. When I trained at Scott Muir's wall in Aviemore I used to start with 20mins of traversing easy stuff with hands and trainers on a vertical wall before picking up the tools.
The Powerball in action.
I have to add, that there are some things I've seen that I truly cannot explain. At last years world championships in Switzerland myself, Rob Gibson and Tim Emmett did what you might call a 'normal' steady warm up for 30mins. Whilst other folks from other countries jumped straight into campusing the tool board and footless traverses of the angled monkey bars. Either they were a robotic super species not yet known about or they were numbnuts. I am still to this day dumb-founded by how you can go from being stone cold to reps of campusing without injuring yourself? Strange.