At my local venue tonight playing a friendly game with my Battlemaster and Assistant Battlemaster we got into a bit of an arguement about Anastasia Kerensky. Even though it doesn't say it on her card does she take heat for each of those extra attacks? I didn't think so, but they thought she did. Since I was out voted on this I went their way and played her with the heat building. Who was right on this one?

yes, she will take a click of heat after each attack.

and just in case you didn't know, her special ability also takes from your total orders. so in a 450pt game if you were to give her 3 orders then you will have used up all orders for that turn. plus the extra heat.

Yep. Here's what the special ability says:

Give this unit a ranged combat order targeting a single opposing figure. If the attack succeeds, you may give it a second ranged combat order. If the second attack succeeds, you may give it a third ranged combat order.

It seems like one of the most common misunderstandings for new players is the difference between orders and attacks. An attack is just part of an order, so making an extra attack does not create heat, but an order really is another order so it does generate heat and cost an order from your order total.

you are lucky that you have a rational and sane battlemaster

the last time I went to an event, the battlemaster was nuts. kept me from ever competing in a venue again