Coldest US cities I worked in were Spokane, Minneapolis, Milwaukee. Hottest Phoenix, Melbourne (AU), Dallas. Nice to be retired here.
Hmm, coldest/hottest places I've been to that were work related visits must be Helsinki and Madrid respectively (business trips). Privately the hottest would be a close call between Death Valley (in early May), the Australian desert and Athens (middle of summer), while the coldest I've witnessed was definitely a winter campsite in the Austrian mountains (-28C). That said, daily work, mostly in a climate controlled office building wasn't all that challenging climate wise.
Coldest and hottest climates I worked in was Afghanistan. Hottest was in Lashkar Gah, coldest was Kabul.
1981 I was in minus 71 (F) wind chill factor while serving as a Soldier at CFB Shilo Manitoba Canada. Hottest place I have been was again as a Soldier and the operation remains classified. It was 121 (F) and 3 out of 16 Soldiers got heat stroke..one seriously! Mother nature may be beautiful in most regards, but she can be unforgiving! In both cases of opposite extreme temperature I did learn 1 thing. I would rather perish by heat than by cold. I have suffered both.
Coldest for me was -69 degrees F while training for our deployment to the Arctic Circle at Ft McCoy Wisconsin. Hottest I am not sure, either desert training in the California Desert (we actually had to leave early because the people who were supposed to resupply us with water failed to do their job and we weren't about to stick around and see who died first) or multiple areas in SW Asia. I don't remember all the temps growing up as a kid in upstate NY, although I remember some days were quite frigid, not not sure they were -69 cold.
Highest I know of was 113f in Oklahoma city, in 2012. The summer of 2011 was harder for me. 63 days over 100f. 21 days over 105f, 3 days over 110f. I was out in it operating a backhoe that year. Coldest was -28f in the Black Hills of South Dakota. Spent the night in my semi's sleeper, with the engine off, due to the fuel gelling.
Hottest I've worked was Ashgabat, Turkmenistan; coldest Fairbanks, Alaska. Coldest in the summer was Shemya, Alaska.
I will put in for highest altitude workplace at 4,600 metres (15,000 feet). Collahuasi Mine northern Chile border of Bolivia just south of Peru. Parts of the mine where I would have repeaters to install would be at 5100 metres (16,700 feet). You pickup a rental truck at the airport at sea level in Iquique and head east for 5 hours and about the 3rd hour mark you wonder why the truck will not get out of 2nd gear when it seems almost flat on the road. Eating lunch at 4,300 metres (14,100 feet) requires you to take long breaths between bites otherwise you get light headed. Mining accommodation is at 3,800 metres (12,500 feet) and they have a high humidity enclosed jungle garden separating the wings, its meant to make it easier to sleep. I would go for 2 weeks stints and have a headache the whole time until I got half way back to sea level.