In the context you have, would die feels more natural. Will and would are both modal verbs, modifying die. Will is used for the indicative future tense--for things that are known (or presumed) to be going to happen: "I will be there at 8." "It will rain tomorrow." Would, on the other hand, would indicate the subjunctive future tense in this context, in which case the verb modified is not necessarily going to happen.
To see the difference between the two we need to recast the sentence a little.
If Bob knew that tomorrow he will be fired...
If Bob knew that tomorrow he would be fired...
The first phrase assumes that Bob is actually going to be fired tomorrow, a fact known to the speaker and the listener, but, presumably not to Bob. The second phrase assumes nothing about whether Bob will be fired.
In your example, using will die implies that the speaker knows that the listener is going to die in a year. Not only would that be disturbing, but it moots the question, since the speaker has now passed on the information that is the subject of the question. Or it could be a clumsy way of breaking the news.
In all seriousness, neither one is actually incorrect, and the listener would (presumably) understand from context that will die is part of the conditional and not a known fact. But technically it would be ambiguous, whereas with would, it is clear the situation described is not real.