Interesting question. Extreme temps (hot & cold) are but one of the causes of climate related deaths, others are wildfires, storms, floods, food shortage, disease etc.

With regard to extreme temp deaths this is latest research on the topic https://www.thelancet.com/journals/lanplh/article/PIIS2542-5196(21)00081-4/fulltext#tbl1

High level extreme cold is causing more deaths at the moment but heat related deaths are rising, especially related to the observed increase of humidity over land which is impacting wet bulb temperatures significantly in many places.

But heatwaves create havoc on the entire system. Check out this graphic where researchers mapped out the impact of the 2022 Indian heatwaves.