Final answer:
To order stars from coolest to hottest based on provided information, Betelgeuse (red) is the coolest, Capella (yellow) is intermediate, and Archenar (blue) is the hottest.
Step-by-step explanation:
To list stars in order of temperature from coolest to hottest based on the information provided, we can rely on the education provided by the Hertzsprung-Russell (H-R) diagram and our understanding of stellar colors. According to the H-R diagram, the least-massive stars are both coolest and least luminous, and are located at the lower right of the diagram. Conversely, the largest-mass and most luminous stars are the hottest and can be found at the upper left. As for stellar colors, they offer a reliable indicator of temperature: red stars are cooler and blue stars are hotter. This means that Archenar (blue) is hotter than Betelgeuse (red), with Capella (yellow) being intermediate in temperature.
Therefore, ordered from coolest to hottest, the stars would be Betelgeuse (red), Capella (yellow), and Archenar (blue).