Hi Melissa, looks like you have a lot of great responses here. As someone who has licensed several products and who coaches other inventors/product developers, I wanted to weigh in.
There are many ways to skin the cat when it comes to getting deals done. In terms of approach, I try to make it as non-adversarial as possible and get them to understand what is fair to both of us...to make it a win-win. Without more information, it sounds like the warmers are the product differentiator here. And frankly, it's hard to separate out the components in terms of assigning a royalty. I would argue/counter to them that this is what makes the whole product and the royalty should be on the final wholesale price.
The Back-up Plan - Plenty of companies make lunch boxes, but it is the warmers that are so unique. So, it's ok that they just want to pay you for the warmers and count that as half of the cost on which to base the royalty, BUT it should be double the royalty they are suggesting (which of course gets you back to your original agreement). Alternatively, or if they balk, I would say, "The original deal was for the whole product. I understand you want to pay me half the royalty, which I don't think is fair...so to make this a win-win, why don't we just make it non-exclusive." And you can even give them a bit of a head-start on any one else you license to.
You can also limit it by retail distribution class or other category, such as lunch boxes. Maybe reserve it for camping or any other use you can think of. I have done that many times....licensing the same product into different categories.
Finally, maybe there's a way to go with what they're suggesting (warmers only) and get a broader deal on the warmers...for their other products, so that you make more than you would have because it's not limited to your lunch box. Maybe they sell more because it goes into all of their lunch boxes and coolers. Or maybe you license them the warmers...and reserve the right to sell the full lunch box with the warmers to someone else (if they're saying that's a different product, that might be the best argument against their thought process of paying just for the warmers).
Obviously, it would help to know more details, such as what the actual licensing fee is that they are proposing...as well as some of the other critical deal points, like minimum guarantees, exclusivity, rights to make it non-exclusive for failing to hit the guarantees, who pays to file the utility patent, defend it, improvements clause, etc.
These are all just thoughts of ways to make the deal more fair and favorable to you. Also, just an fyi, I'm also an attorney who has negotiated and drafted many, many agreements over the years.
PS Sorry for the length of this, but hope it helps. Good luck!!!