My front lawn has suffered badly with "dry patch" following last Summer's heat; dark areas of dead turf, that don't regrow. The thatch has become water repellent, so it's bone dry underneath, yet wet and mossy on the surface. My lawn has all the warning signs: sloping site, sandy soil, full sun and an old lawn.
To try and restore it, I started by spiking it all over with a garden fork last Autumn to let the water back in and relieve any compaction.
At the end of October I applied "no rake" moss remover pellets, which contain a bacteria to eat the moss and thatch. This might seem an odd time to apply them but it was wet and very mild (above the 10c that the bacteria need to work), and the weather stayed mild throughout November. This seems to have made a big difference to the dead thatch; before it was very fibrous and hard to dig out, now it is much weaker and almost lifts off in places.
I gave the lawn a hand raking during the warm spell in February, and in some areas the thatch just crumbled off leaving bare patches.
I've been reseeding patches since last Autumn, even during mild spells through Winter, and I'm doing a lot of reseeding now. I'm using a knife to lift the dead thatch off, working around and leaving any grass that's still growing. It seems to pick up once the thatch around it has been cleared, and I'm hoping it will spread back into the bare areas.
There's quite a lot of advice on line e.g. the RHS website, as a result of which I'm going to start using a lawn wetting agent, which is apparently what a lot of professional groundsmen use.