The usual heat transfer issues all apply.
What are those? Well, let me see
The handle will warm up until it's total heat losses equal the total heat coming in.
Heat comes in mostly by conduction from the body of the pot.
Some materials conduct heat better than others. Metals tend to have high thermal conductivity (with aluminum and especially copper begin particularly good at it). Plastics and wood tend to be poor thermal conductors.
Thick pieces of material can conduct heat faster than thin ones, but they also take proportionately more heat to increase the temperature, so this is a wash...unless you connect a solid handle to the body with thin spars (as in your upper photograph).
The handle loses heat to the air by conduction (very little), convection (much more), and radiation (very little until it gets to hot to hold). For all of these having lots of surface area improves the rate at which heat can be dumped into the surrounding environment.
Shape and orientation matters a lot to convective heat losses, but the dependence is too complicated to describe in a few words.
I find that bent sheet metal handles tend to stay cool, while solid handles get hot. If the half-n-half version you describe above has a pretty solid piece of metal that that part will behave very much like a all-metal handle (it may even be worse as the teflon will insulate the underside).
Short of taking detailed photos and constructing a model in a thermal simulation there is no rigorous way to know in advance. Still, if you've been cooking for long you probably have some intuition in this matter. Trust it.
You're going to die horribly from cooking in a rusted pan!
Just kidding! A little iron in your food isn't going to hurt you, and can actually help prevent anemia. To quote On Food and Cooking (pg 790): "Excess iron is readily eliminated from the body, and most people can actually benefit from additional dietary iron."
Now, to back this up further:
You won't get much iron out of the pan unless you cook something acidic in it. Rust is insoluble in water without acid present, and in order to become soluble you have to convert to iron nitrate, sulfate, or chloride, according to the solubility table. Nothing you cook in there is likely to cause the necessary reactions to render it highly soluble.
I found a source quoting specific numbers for iron from cast iron cookware, if you are concerned. The gist is that most cooking in cast iron added from 1 to 5 mg of iron to the food, with the highest numbers coming from acidic foods with tomatoes. Applesauce was the highest, good for about 7 mg.
This level of iron intake is quite safe and healthy. To give you a point of comparison, the FDA suggests iron intake of 8 mg/day for men, and 18 mg/day for women, and 80% of the world may be iron deficient. Iron toxicity occurs at about 45 mg/day. So, as I initially stated, you're perfectly safe cooking in your cast iron, and are probably helping your health rather than hurting it!
Best Answer
Incomplete common sense answer (no idea about local regulations. If this should have been a comment, somebody tell me! :) People breathe in kitchens while there are open pots, and blowing is a form of breathing. Food is not ever considered completely sterile unless pressure cooked/canned, cold sterilized (chemically or by pickling in extremely harsh pickling solutions), or irradiated. Also, unless things are served straight after that, they will be rather thoroughly cooked in the depicted scenario - if there are germs in that breath, they are cooked to death; spores will not matter much with food immediately served; if there was poison the cook would be dead or ill too. Virii could be a problem too,