Can pH levels go beyond 14?

pH levels can surely go beyong 14 . if you check out some lower level books , you'll find 'pH range 0-14' but that doesn't make any sense.
pH varies from 0-14 at 25°C .
While reading one of the experiments in my bogus'lab manual ', i found pH of water at temperature more than 25°C to be less than 7 . But those books don't print why that's so.
The pH decreases on imcreasing temperature but yet steam isn't acidic . That leads to a practical conclusion that pH isn't static or say it doesn't has fixed range.

We know , pure water is neutral which means
pH = pOH.

therfore on adding both these we get the pH range .

Those rotten books print 'increase in #H^(+)# ions' as it's cause but don't really justify it .

Well, this was that pH range could contract and as per the question we gotta answer something different.

Now, pH could also be more than 7 (of pure water) but how?
That's the same answer as we have when we increase temperature .
with this i would conclude
pH is inversely proportional to #delta temperature#

Now , this was all like postulates without any justification .

Lets move to another question 'why does temperature have any effect on pH?'

The answer is related to concentration of #H^(+) & OH^(-) # ions [note #H3O^(+) & H^(+)# are one and the same things.

Throught several experiments it was found that the concemtration of Hydronium ions and hydroxide ions both is #10^(-7)#M each . (conclusion water is neutral)

but as soon as we increase the temperature the rate of forward reaction increases or say the equilibrium shifts #H2O# breaks down into its respective conjucate base and acid [ions] thus there is an increase in concemtration of ions .
suppose the concentration increase from #10^(-7)# to #10^(-5)# .
this increase will be pf both cation amd anion thus solution stays neutral.

at 25°C
Kw =[#H3O^(+)#][#OH^(-)#]
Kw = #10^(-7)# × #10^(-7)# =
#10^(-14)#
Now if you want to find max pH its
-log (#10^(-14)#)=14
but as in the example we took
the concentration to be #10^(-5)# . so using the formula we get max pH as 10 . similarly we could also increase the ph range decreasing temperature.
Here's a link which includes some example and also explaination
https://chemistry.stackexchange.com/questions/6997/ph-range-outside-conventional-0-14
cheers!