If you want to invent your own custom laws of nature, any of them can make sense. You just have to invent a set of universe with coherent laws of nature in which "life energy" or "luck" is a real, quantifiable thing. If you do this, decide on some rules that make sense and stick to them strictly. I'll write the rest of my answer assuming you mean which of the three makes the most sense assuming the laws of nature as we know them, i.e. which makes sense to someone living in the real world.
1) It makes the most sense to expand heat to be energy in general, as the word is used in physics (i.e. not "life" or "luck"). Allow the energy to be drawn by means of a link to the future which is attached to a specific object, whether that object be internal or external to the caster's organism, manufactured or naturally occurring. Then when energy is channeled, let that energy be taken from the source that has the highest net potential energy in the immediate vicinity of the future version of the linked object. If at that future time the link is immersed in heat or light, there will be a transition to cold or dark. If the place is already cold and dark, then the binding energy in matter can be used and future objects disintegrate.
The caster can't choose the time from which he draws, but the distribution of times can favor certain time frames. In other words, occasionally the time frame could be a few seconds or a few millennia, but in general it is a few years or however long you as the creator want. In the event that you want to explain this randomness, you can give some hand-wavy pseudo-scientific explanation based on over-simplified quantum mechanics.
Because the effect would always take place in the vicinity of the linked object, and assuming that the caster would want to always have his amulet/wand/whatever on hand, the effects would always affect the caster's future, sometimes to the point of damaging his body or possessions.
2) If you wanted to assume some kind of non-local hidden variable interpretation of quantum you could do luck as a manipulation of these hidden variables to affect probability. Then magic is just manipulating probabilities of microscopic natural events to get your desired event, however unlikely, to become the most likely outcome of a situation.
This could require your mages to be intellectual in order to understand the inner workings of the thing they want to affect. It would also require greater focus and mental power to process the probabilities involved in larger/complex spells.
If you want this to be linked to the future, you could say that this adjustment of probability makes it harder for less likely things to happen in the future, amounting to a drop in future luck (or an increase if you are trying to avoid an unlikely death). This would be believable enough for me if explained in terms of quantum effects, but I would still prefer the previous solution.
3) Lastly, if you really really wanted to do life, you could justify it by saying that your original mages created a "machine" that communicates with the mages and translates their commands to physical effects in the world but takes from them physical health. Then when they cast a spell they are actually communicating their desires to this "machine" which then accesses their part of the world from a distance and causes the desired effect. To me this would be believable enough but would sound silly, and I would be left wondering who the sadists were that thought that life would be a good currency for magic. It would also allow for mages who study the machine instead of studying spell casting to "hack" the machine and do whatever the heck they want, defeating your purpose in making magic consume life-force. Basically, the consumption of life would not be fundamental to magic.