The absolute pressure of a sealed gas is proportional to its temperature in kelvin: heating a tyre from 20 °C to 50 °C raises its absolute pressure by 10 percent, and doubling it takes 586 K, which is 313 °C.
Hotter molecules hit the walls harder and more often, and the pressure is in proportion to their mean kinetic energy, which is in proportion to the kelvin temperature (Gay-Lussac). A tyre at 2.2 bar gauge, which is 3.2 bar absolute, at 20 °C reads about 2.5 bar gauge at 50 °C, which is why a tyre is checked cold.
The volume and the amount must be fixed (a tyre grows a little as it warms, and it leaks), and the law needs absolute pressure, not the gauge reading above the atmosphere. A gas that can condense, like steam, does not follow it near its boiling point.
Estimate with the rule, then check it against the calculator that models it properly.
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