We ended up taking the metro and walking with our suitcases to the hotel. Yes it was hot, but nothing life threataning :-) I actually enjoyed the heat . Felt different and unique which is the whole point of travel ( seek out new experiences )...
One day we even walked 5-6 miles in this 110+ heat ( but in the late afternoon ). Also went to the Doha Sands beach. Water was hot, but enjoyable. Felt like a hot tub or something..But the breeze felt cooling, even though the temps were high.