Temperature effects on pKa and pKw
The background of the topic is, that for the function
$$y = \frac {a(T)}{x}$$
$y$ does depend on $T$, but $x$ does not.
$\mathrm{pH}$ of basic solutions is temperature dependent via $\mathrm{p}K_\mathrm{w}$ temperature dependance.
Additionally, $\mathrm{pH}$ of weak acid/base solutions is temperature dependent via $\mathrm{p}K_\mathrm{a}$ or $\mathrm{p}K_\mathrm{b}$ temperature dependance.
There is also additional, difficult to quantify factor of temperature dependency of activity coefficients.

The $\mathrm{pH}$ of strong acid solutions ( like hydrochloric or sulphuric acids ) of molar concentration $c \pu{[ mol/L]}$ is approximately(*)
$$\mathrm{pH}=-\log{c}$$
( For sulphuric acid, it is more complicated due 2 acidic hydrogens, where the second one is not strongly acidic ( in sense it has considerable $\mathrm{p}K_\mathrm{a}$ )).
The $\mathrm{pH}$ of strong base solutions ( like sodium hydroxide) is approximately
$$\mathrm{pH}=\mathrm{p}K_w(T) + \log{c}$$
because concentration of hydroxide ions $\ce{[OH-]}$ is the same as the concentration of e.g. sodium hydroxide. Concentration of hydronium ions $\ce{[H3O+]}$ then follows the above $y = \frac {a(T)}{x}$, i.e. $\ce{[H3O+]} = \frac {K_\mathrm{w}(T)}{\ce{[OH-]}}$
The $\mathrm{pH}$ of weak acid solutions ( like acetic acid ) is approximately
$$\mathrm{pH}=0.5 \cdot (\mathrm{p}K_\mathrm{a}(T) - \log(c))$$
The $\mathrm{pH}$ of weak base solutions ( like ammonia or sodium carbonate ) is approximately
$$\mathrm{pH} = \mathrm{p}K_\mathrm{w}(T) - 0.5 \cdot (\mathrm{p}K_\mathrm{b}(T) - \log {c})$$
The neutral $\mathrm{pH}$ is then
$$\mathrm{pH}_\mathrm{neutral}=\frac {\mathrm{p}K_\mathrm{w}}{2}$$
Note that if there was an OH- electrode, situation would be the opposite. Strongly acidic solutions would have temperature dependent pOH and strongly bases would not.

For the strong acid/base $T$ dependency, see the table:




t[deg C]
pKw
Solution
pH
pOH




25
14
0.1 M HCl
1
13


25
14
0.1 M NaOH
13
1


50
13.27
0.1 M HCl
1
12.27


50
13.27
0.1 M NaOH
12.27
1




(*): The equations are not exact, as there plays the role also the ionic strength, activity coefficients and for weak acid/base cases the simplification of $\ce{pH}$ calculation.