I really don't know what the ambient air temperature was during my time on Denali, but it's largely irrelevant. The weather report may say 25 or 40 or whatever, but the actual temperature felt, at least during the daytime, is entirely dependent upon the sun and wind. You could pretty much count on it being cold in the early morning and late evening, when there wasn't direct sunlight (it doesn't get completely dark at this latitude in mid-summer, the sun just goes below the horizon a little ways for a little while; it's still light enough to read at 3am), but with more intense sun at this latitude and altitude, along with the reflection from the snow, it can get blazingly hot in the afternoons. Then, if clouds rolled in or the wind picked up, the temperature would drop quite a bit. If you were out of your tent for a while (ie dinner), you'd need to bring an extra layer in case it got cold while you were out.
Because of the intensity of the sun, protection from it is a must. Sunscreen must be applied constantly. Sunglasses (specifically glacier glasses, with a heavy tint and protection on the sides and bottoms) are worn almost all the time, even in the tent when it's super intense. Snowing? Wear glasses. 4am leaving camp? Better at least have your glasses at the ready, but may as well put them on. Typically glacier glasses are polarized, so they help you make out features in the snow, so it never hurts to wear them.
The afternoon heat also make for poor travel, when the snow gets soft and slushy. On the Kahiltna, which is already one of the most dangerous parts of the trip, soft snow increases the risk of falling into a crevasse. This is why we did that portion at night, giving the snow a chance to refreeze. The afternoon melt also affected camp life, making things icy in the late evening and early morning. This is why it was not recommended to walk around camp in boot liners or booties.
We had snow numerous days on the mountain, only once did it get more than a couple of inches of accumulation. Snow, by itself, did not stop us; it was more wind or low visibility that caused us to hole up in camp. It was high winds along the West Buttress that forced us to spend an extra day at 17,000 camp. The following day, it was snowing, but the winds were much lower; we also wanted to get down before snow accumulation caused avalanche danger. That was the one storm that made for real accumulation; it forced Dave Hahn's team (the RMI team that flew on a week after we did) to wait at 14,000 for the avy danger to come down (by melting and otherwise consolidating). There was about a foot of fresh powder on motorcycle hill when we descended to 11,000 camp from that storm.
The strangest storm by far, not just for our trip but for the Alaska Range in general, was when we first got to 14,000 camp. After we set up camp and were resting, there was some rumbling. This didn't seem unusual at first, there's constant rock and ice fall (close enough to hear, far enough to not be a danger). But then it was too frequent, and it became clear that a thunderstorm was rolling in. For us it wasn't that big of a deal, we were safely in our tents, but it was a very big deal for the teams that were high on the mountain making their summit bids. There were reports of skis and pickets arcing. Everyone that was up high had to hunker down and retreat to high camp. Some ended their trips after that, others waited and made another summit attempt. Mike Haugen's team (the RMI team that flew on a week before we did) retreated in the storm, rested a day at high camp, and then successfully summited the next day.
While being stuck in a tent on a weather day can be mentally challenging (boring, frustrating), by far the worst weather delay was in flying off the mountain. Because the bush planes fly visually and have a 10,000-foot ceiling, they can't fly through clouds. For us, sitting at the landing strip, we had no idea if there were clouds in town or anywhere between here and there, we just saw that it was clear and sunny on the glacier. It would have been worse being Haugen's team and being stuck for 6 days, but at least the weather was crappy everywhere, so they knew they weren't about to be picked up. To add insult, not only was it nice on the glacier, tourist flights from another plane company were landing. We kind of felt like the animals in a zoo (and probably smelled about the same after 20 days without showering).
Basically, if you've ever been somewhere that they say "If you don't like the weather, wait 5 minutes," they have nothing on being on a glacier in the Alaska Range. It can go from sunny and 80 degrees to snowing (and still sunny) to cloudy, windy, and 50 degrees in a few minutes.