Temperature threshold of a cell
Talking about cells in general, the main problem about higher temperatures is the denaturation of proteins (when proteins lose their structure and then they don't work anymore), and every organism has a specific range of temperatures in which its proteins have evolved to work in that determined range.

The most common example of bacteria living at high temperatures is Thermus aquaticus (or others) which proteins are widely used in laboratories for their peculiarity to be able to work at more than 70 °C (e.g. polymerase chain reaction).

In humans the mean temperature is 37 °C, and it's not unusual during severe fevers to get it rising to 39-40 °C (so the assumption that over 39 °C occurs death is incorrect). Of course you can reach higher temperatures but reaching 43-44 °C leads to multi-organ damages. You can find out more in this review.

Another thing to take in consideration is that cells must contain water in liquid phase, so over the 100 °C limit (at atmospheric pressure, so the limit can increase alongside pressure) it's kind of impossible to find living cells.