A pretty good rule of thumb is whatever the temperature is forecast to be in Phoenix is probably what you'll see at the bottom of the canyon. Whatever the high temperature is for the North Rim figure it's probably going to be 25-30 degrees warmer at the bottom although it could get hotter than that. So if the high is forecast to hit 75 degrees on the North Rim you're looking at temperatures of 100+ at the bottom. If it's forecast to be 105 degrees in Phoenix it'll probably be about that at the bottom of the Canyon

Are you doing this as a day hike or are you planning on doing a couple day backpacking trip? You can use this as a guideline for what temperatures will be at different points along the way. For example, the North Rim trail starts at about 8200' and drops to Phantom Ranch at around 2500'. Along the way you'll pass Cottonwood Campground at an elevation of 4080'. A normal rule of thumb for the Sierra is about 3 degrees per 1000' but during early October in the Grand Canyon I'd put that number at closer to 5 degrees per 1000'. So if it's 60 degrees at the trail head figure it's about 80 degrees at Cottonwood or Indian Gardens at 3800'. These numbers aren't exact but that'll give you a good estimate of the range of temperatures to expect.