Standing in a chilly pitlane at Silverstone between sessions discussing tyres with the clients engineer it brings home the importance of the black, round things in the corner.
Take time to learn the tyre you are running on: what pressures do they like in what conditions; how many heat cycles can they take?
Running on the wrong tyre at the wrong time is pointless, no point pounding round on tyres past their best, you will learn nothing and the risk of a loss of control is much higher. Put the right tyre on in and one that is in a good condition. A new tyre is expensive but cheaper than a repair bill.