You are even allowed to put 90 psi cold in them if that is needed.
The 80 psi is called the maxloadpressure or reference-pressure( further Pr for pressure reference) and is not the maximum cold pressure of the tire ( further Pmax).
From C-load always the Pr is written on sidewall , but for standard load /P-tire and XL/Extraload/reinforced the Pmax is written on sidewall. The Pr is SL/P-tire 35psi/2.4bar and XL// 41psi/2.8 bar for American tires, Europe a little different and some exeptions.
Once determined by and article of Semperit(continental) that the Pmax cold is 1.4 times the Pr cold.
So your tire can stand even 1.4 X 80= 112 psi cold. Also the valves are given cold maximum pressure in their standards and a normal rubber valve can stand 65 to 70 psi cold and may rise to American mildest standards to 26psi/1.8 bar higher so 91 to 96 psi warm.
This is needed because when severe braking the inside tire temperature can rise incidentially to even boiling point of water, and with that the pressure rises that 1.8 bar.
You probably have metal valves so they can stand the pressure even more ( above 10 bar / 145psi) but Highpressure rubber snapp in valves from the TR600HP series can stand a cold pressure of 6.3bar/95psi to mayby 6.8bar/100psi depending on the brand. Probably even more psi rising for warm , but I dont have the standards for them given.
So dont be afraid with the pressure and never bleed air when warm.
Best would be to give the tire a pressure that is save for it at the coldest outside temperature you ever get in , so then its still save.
Then when outside gets warmer, you have higher pressure but still within the limits so you wont get terrible bumping, and within the limits of what tire organisations allow.
Also look at my opened topic about
Comparing tires for replacement