In the case of Liebeck vs. McDonald’s Restaurants, P. T. S., Inc. New Mexico District Court (1994). How would you have gone about arguing that your client had not committed negligence, or if you are the plaintiff, how would you have more strongly argued that negligence was committed by the defendant? Please focus on the specific elements of negligence as to why the case was won or lost by a party.

I'll give an explanation for both sides, because it is an intricate and complicated case. The repercussions of this case created many changes, and it is frequently regarded as the hallmark of overreaching litigation in spite of the fact that the woman in question was severely injured by the coffee.
On the side McDonald's and why they did not commit negligence:
The defendant produces millions of cups of coffee daily for individuals all around the globe. This coffee is kept at an operating temperature of about 180–190 degrees Fahrenheit, and yet relatively few individuals are ever burned by it (estimates say that at the time, around 700 individuals had experienced burns from the coffee, compared to the millions of drinkers). Statistically, this amounts to a fractional minority, which represents the frequent injuries anyone encounters performing routine tasks, especially caused by operator error. Additionally, each cup is marked with the words "Caution: Hot Beverage" as a warning to those consuming it. This should be enough to deter anyone from unsafely consuming the beverage.
As a final note, it is clear that the plaintiff, Mrs. Liebeck, had opened the beverage in a moving vehicle. This is an unsafe and inadvisable practice that McDonald's certainly does not condone. We believe that the primary responsibility for the injury is Mrs. Liebeck's improper use and transport of the beverage.
In the defense of Mrs. Liebeck:
While it is noted and accepted that Mrs. Liebeck opened the beverage container in the car, typical hot beverages are served around 150–160 degrees Fahrenheit, a significantly lower temperature. These temperatures, while still dangerous, take much longer to cause severe (i.e., third-degree) burning (in the range of 20–30 seconds), whereas the coffee supplied by the defendant has the propensity to cause severe burns in around 3 seconds, even through clothing, not allowing the plaintiff ample time to remove the hot liquid from herself. Additionally, the caution statement on the container implies that it is hot, but makes no mention of the dangerous nature of the beverage, nor how severe the burns could potentially be.
A final point should be made that, while 700 individuals experiencing burns is apparently statistically insignificant, it still represents many people who have received harmful results from the products supplied by McDonald's. It is the duty of the corporation to ensure that their products are not harmful, and it should also be noted that in many of these cases, the individuals were likely not driving in vehicles, nor were they opening the container, thus affirming the inherent danger of the product itself, as opposed to the improper use of Mrs. Liebeck.