I use timeanddate.com. It goes back to 2009, and you can check daily weather hour by hour. The information also includes humidity, wind speed and direction, etc. It's been very helpful in deciding when to visit, whether I need AC, what to pack, etc.
We stayed at The Randolph Hotel by Graduate Hotels in Oxford in June 2022. While the rooms were air conditioned, the bar and reception rooms were not. I love Oxford. Hope you have a great time.
Addition: In September 2023, however, we were in Paris mid-September with temperatures of 95 and 96 for a solid week. Fortunately, we had rented a flat with AC AND a fan (unheard of). We also had a washing machine which we used to wash our very sweaty clothes and bath towels, daily. I showered three times a day first one after getting up; second, after having been out in the morning (afternoon shower) and evening (evening shower). So, you are correct about the possibility of hot weather.