I find they affect my tyres quite significantly.
In qualifying for example, if its pretty hot, they get up to temperature a lot quicker, and I also find there is more grip too. However, they only last for 2-3 laps before they drop off quite a lot.
In race, naturally, if the ambient is hotter than normal, it will have an effect on your tyres too. You can probably guess the rest of what I am saying though: the hotter it is in ambient, the faster your tyres will degrade over a race period.
If its cooler than normal, then it will be harder getting temperature into your tyres, so may take a lap or two to get them up to optimum temp. In race, it means your tyres will last slightly longer, compared to if it was a little warmer.
With all that said, just bear in mind that this is from my own experience.