I definitely wouldn't use time-out for whining. (Thus far, we haven't used them at all, and don't have plans to, but that's another topic...
) If ds is whining about something that he *can* have/do, then I encourage him to "say it in a strong voice." If he's whining about something that I'm not going to say yes to, then I acknowledge his desire (e.g., "I know, you want the (whatever), and Mama said no.") and offer sympathy that he's upset/disappointed/mad/whatever about the situation (e.g., "You're very (whatever) because Mama said not now. It's hard to wait."). I'd do that if it evolved into crying, too. The whining/crying isn't working to get him whatever it is that I said no to, but I'm acknowledging his feelings. (Although, if it's something that I said no to in a reflexive way, without realizing how important it is to him relative to how unimportant it is to me (like, say, if he asks to do playdoh and I'm not really in the mood), in which case I'd realize that quickly and say something like, "Mama didn't know that it was so important for you to play playdoh now. Can you ask me again in a strong voice?")
Some people might suggest that this method of acknowledging the feelings behind the whining is giving attention to an undesired behavior, and that the whining will increase as a result. (I don't mean that the OP or PP would necessarily say this. I mean, if I were to describe it to 100 random people.) The thing is, though, if a child is whining to get attention, then I think the problem that needs addressing is that the child needs more attention, and to learn other, more appropriate ways of getting it. With those appropriate techniques in his/her repertoire, the whining *will* drop out over time.
Ds generally only whines now when he's tired, and it's actually usually for things that he can have, but since he's tired, it's like he doesn't realize that he hasn't already asked for them. He seems to be upset because we haven't read his mind.