The heat you're talking about is a notch higher than I've dealt with; last summer I ran outside several times at 91º F (33º C) with high humidity. Sometimes I crapped out of the workouts, like getting 11 miles of the planned 14 miles of tempo intervals done before I had to quit.

The interesting thing is, late in that summer I ran a 5K. It wasn't all that hot by the standards of what I'd been training in, 68º F (20º C); but it was terribly humid. I turned in a PR time, just thought of it as a 3 mile interval with a stride at the end. Guys who had trained a lot in the air conditioning faded after 2 miles, but 3.1 miles wasn't enough for the humidity to catch up to me.

I'm not sure how much of this applies to your situation. 40º C might be enough hotter that it's not just uncomfortable, but also physically dangerous. But I'm sure the treadmill is a lousy substitute for really running long. If Galloway walk/run intervals make dealing with the heat possible, I'd want to be outdoors. Perhaps someone who uses the Galloway method could comment on that.

Is there an indoor track you can use? In the other extreme of weather (30+ mph winds, 7º F / -14º C, water bottles would freeze solid within 10 miles), I once ran 22 miles on a 200 m indoor track. That had its mental challenges, but it was better than using a dreadmill. I knew I couldn't keep track of 177 laps, so I lapped the Garmin every 8 track laps, and essentially treated it as 22 x 1600m easy, with no recovery and a 200 m extra to make up the difference between 1600m and a mile. I could keep track of 8 track laps, and I just let Garmin count how many of these 1600m sets of 8 laps I had run.

I don't handle humidity well, so in summer I do a lot of miles on the TM. Running at night works here, but may not be safe in the Middle East. I run on the TM in Winter too, if there is a lot of snow and ice making the roads dangerous. (If there's no shoulder, I'm not running on it.) I have done 20 milers on the TM by watching movies or a good TV series. In some ways it's easier because I keep the pace slower than I normally run outdoors. I usually do a progressive run, switching up every 2-3 miles. The first couple of times were hard, but I got used to it one very bad winter when I was training for a Feb. race.