Q:

Critical temperature what a family house's average thermal energy storage can ride out? 

Lets say average family house was built with brick (EU).  
We know that brick has a good mass of thermal energy storage.  
So in the night, when it is colder, it can store lower temperature thanks to its mass.  
During daytime on summer, when it is horribly hot outside, it can still give lower temperatures, stored from the night.  
But with this climate change, maybe things are getting warmer and warmer.  Ex.:  35-40 Celsius in the shade.  
I am not thinking of precise answer regarding exact temperatures, but an about average, that in theory, is it possible or not.  
->
So the question: could it get so hot outside, that building buildings based on great mass will be the past?  
So a building, what is in a very hot area (and cold on winter, like -2 Celsius average) shouldn't have great mass, rather very-very-very-VERY good insulation and air tightness?  
I think when it is hot for several days, the great mass is not enough to survive.  

A:

When a person builds a building with brick (say, in 1890), they are not engineering the building for thermal management.  They are using brick because it is cheap, durable, and holds up the roof.   
While the brick could be a thermal management asset, it is only by dumb luck.   If you want more effectiveness, you need to actively engineer for it.   
Right now, when the sun goes down, the brick radiates its heat in both directions - into your house and out of your house.   It actually does the second one better, since it's in direct contact with outside.   After the brick cools down, it then becomes a conduit to draw your expensive interior heat to the outside.   So while it is thermal storage, it is also a thermal pipe.   
What you need is for the thermal storage to last longer and stop being a pipe.   The best way to do that is put insulation outside the thermal mass.   In other words, wrap your building with insulation.  
And then, add either active piping (solar thermal, ground source etc.)  or passive solar design (well-aimed windows with summer shading, however, it doesn't sound like you're building a new house). 