Question is 76c too hot for i5 3470 on gaming ?

Aug 27, 2022
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hey, i recently bought an Core i5 3470 and i think this cpu is run very hot
my idle temps are betweeen 50-55c
and when i open a game like gta 5 ( on very high settings ) it goes up to 76-78c
i opened cpu-z cpu stress test and see the same temps

i have original intel stock cooler

its necessary to buy a air cooler ? or no ?
 
actually, i dont have any case fan on my system
but my old cpu ( pentium g850 ) temps are good, max 69c
after i upgraded to new cpu ( i5 3470 ) i have high temps like this
idle = 50-60c
+80% usage = 70-80c