Your expectations are "reasonable." Last year, highs for October 5-9 at West Yellowstone were in the upper 60s (maybe unseasonably warm?)
Weather reports from October 2020 in West Yellowstone, Montana, USA with highs and lows
www.timeanddate.com
A week later, a cold front must have moved through and temps were 20 degrees cooler, with highs in the upper 40s and 50s -- what you are expecting.
A bigger concern than the weather might be what services are still open in Yellowstone in early October. Most of the restaurants have closed, so bring your own lunches and plan on a restaurant in West Yellowstone or cooking dinner back at the condo. Super Valuable info on that here:
On the very, VERY plus side of the equation, the uncertain weather and limited services at Yellowstone in early October definitely cut down on the tour buses and outrageous crowds seen in summer season.
Always good advice: Spend a few hours on the internet well before your vacation to plan what you want to see (no way to see everything or even 25% of Yellowstone in a few days). Leave at or near dawn if you want to find parking at crazy busy places like Grand Prismatic Spring or Morris Geyser Basin. Lots of parking at Old Faithful, so the time of day you are there will not matter; work that into the busy park hours of 10 a.m. - 3 p.m. Same with the Yellowstone Falls area.
Perfect for October would be a trip to Lamar valley arriving within a couple hours of sunset to definitely see a lot of buffalo and maybe see the wolves (ask a ranger at the Albright Visitor Center in Madison Junction where to look - rangers at Old Faithful might know, too). Upper Lamar valley is about a 2.5 hour trip from Island Park, but you could try spotting wolves in Upper Lamar valley until near sunset and still make it back in the dark to Island Park for a later dinner. While nothing as spectacular as the geyser basins, Lamar valley was a very pleasant drive away from the crowds (we saw a momma bear and two cubs just south of Madison Junction on the way to Lamar valley), and we were rewarded with sighting the wolves on our trip in 2016.