The tyre compound contains a catalyst that reacts with the tyre and heat to make the rubber sticky.
The blueing indicates it hit the temp to trigger a proper chemical reaction in the catalyst.
The stickier the tyre the more catalyst it has but the faster it uses it. A race tyre might be good for about 20 or so heat cycles hence why race tyres "go off" without really being worn out.
a heat cycle will be out of the optimum heat range and back in again which is why racers use tyre warmers etc and try to keep their tyres warm and weave when a pace care comes out because the temp dropping would knock another heat cycle out of the tyre.
The presence of the blueing means you got your tyres nice and hot and were
using all the grip but ultimatly shortens the life of the tyre. You generally wouldn't see it on a tourer tyre etc because the reaction is much smaller hence they are not so stucky but last much longer.
How many heat cycles a sticky road tyre is good for i have no idea. quite a few i would think but not hundreds, 40 / 50 :dunno