K-means clustering to separate temperature vertical profiles
here is my 2 cents: k-means is an unsupervised method and therefore it's best suited if you wanted to explore the optimal number of clusters the temperature can be split, this could be useful to see that maybe there is more regions other than east or west were the temperature is different like north and south and you could use a silhouette score or elbow curve to find the optimal number of clusters.
But, what you describe here is a supervised classification problem where you already have the labels(east and west) and want to separate the temperature accordingly, depending on the type of data I would recommend a classification algorithm such as k-nearest neighbors
you could use k-means with a fixed number of clusters, in this case 2, but it would not be as effective as a supervised algorithm