Ok, that still doesn't answer the question of why a small average rise in temperature would lead someone to expect a large rise in peak temperature. Is it possible to make the statistics work? Yes. Is it likely to happen this way? Not as far as I can tell.
How much has the temperature increased so far? Lytton broke the previous record by 4.6 degrees Celsius(!). Clearly the world hasn't increased by 4.6 Degrees so the peaks are much larger than the average increase.
As more energy enters the system is gets more turbulent, leading to wild swings up and down with greater extremes at both ends. Normally stable systems are becoming wildly disrupted.
"The North Atlantic Jet Stream fluctuates between the Balkans to the south and Scotland to the north. Some 300 years of tree ring samples taken in both places show that the jet stream has become far more variable in the last six decades and more extreme in its positions, which results in more severe climate events and a more rapid shifting between extremes on yearly, monthly, and weekly timescales."[1]
This is just weather. Zoom out to chunks of thirty years to say anything about climate. It's akin to saying warming is overblown because there was a big deep freeze this winter. We saw -38C which was a record low since my thirty years in Alberta.
This is an expected effect of climate change. It's not evidence of climate change, and I wasn't claiming it as such, but it is a possible result of climate change.
Have you read much about climate science? The IPCC Summary for Policymakers report is a really great introduction to what's happening: https://www.ipcc.ch/srccl/chapter/summary-for-policymakers/ Relatively easy and quick read, with references back to the full report if you'd like to go deeper on some topic.
I've read a bit about it. I'm aware that there will be more heat waves, but I have seen no expert claim anything remotely like 150F. There are concerns that some parts of the world will begin to exceed a wet bulb temperature of 98 degrees more regularly, which would be very bad, but still a far cry from actual oven temperature heatwaves.
It's worth remembering it's also an unfolding situation, and what I mean to say by that is if you think a 65c peak is unlikely then unfortunately there's no-one you can ask that can give you a totally verified answer. Even still only 5c above current peaks in some places puts us at 55c which is pretty bloody spicy. At that temperature you need to be actively protecting yourself, even a healthy adult might not survive a wave without some kind of proactive protection.
Given that I live in a very hot climate, which already hits 45-50c each year, I'm sitting in the "Better safe than sorry" camp and I am thinking about precautions I can take to make sure me and my family stay healthy long term. One of the longer term thoughts is making sure it's possible to move if it looks like the climate will become particularly challenging.
Yes. Possibly the most devastating effect of climate change is going to be the social/political impacts of the upcoming climate refugee crisis. If you think your right-leaning neighbors are unhappy about immigrants now...
As shown in this article, we're seeing heatwaves in the 120F range now, with "only" 1C increase in warming. While I can't find any specific estimates in the IPCC reports (section 2.2 in the full report seems the most relevant section), the report frequently mentions more extreme heatwaves. It doesn't seem radical to me as an uneducated observer to extrapolate that out to 150F with another 2-3C increase, especially in the context of a casual conversation like we're having here.