I've been to Sardinia a few times, but always in June/very early July. I generally stay in Gallura (the northernmost tip of the island) either in or near Santa Teresa, an area which I love. The weather is not oppressively hot, even in July because the coastal locations are very breezy. Crowds are really limited to July and August, particularly Mid July to end of August. During the month of June sea resorts and beaches are not crowded at all. But I bet that even in August you can find secluded spots because there are so many wonderful beaches and the island is huge. I've never gone there in August, even when I lived in Italy, Of course there might be places busier than others, but from what I hear from my friends in Italy who have homes there, Sardinia doesn't get as crowded as many places in the mainland. I doubt you would experience the mobs of the Riviera Romagnola (Rimini area), or the Versilia (Viareggio to Forte Dei Marmi), or the Ligurian Riviera (Cinque Terre for example).
If you go in late September it's probably not only not crowded but totally dead, except for the largest towns where there is a significant local population. Obviously tourists will be all gone by then because schools in Italy start by early September (actual date varies by region) and in Northern Europe even earlier (end of August). There is no significant non-European tourism in Sardinia, the only Americans I used to meet where serving at the La Maddalena NATO nuclear submarine base (which has been closed since 2008).
If you can go in June, I definitely recommend it. The weather is great, days are long and it's early enough in the season so that you won't find crowds. Prices are also lower, although they start climbing up gradually starting from the 3rd weekend in June up to the exorbitant prices in August.
If September is the only time you can go, then it is best to go earlier rather than later. Crowds will be largely gone after the last weekend of August but nothing will be shut down as yet. The weather will likely be warmer. Sardinia is not that easy to reach therefore you won't see the accidental tourists that might go there just for the day or the weekend, like you would see at any place in the mainland. If one lives in the main cities of the mainland one can reach the closest coastal resorts in less than two hours. But the trip to Sardinia is too long to just go there from the mainland for a weekend, therefore tourism is the island is limited to those who go there for extended vacations in summer, weekend travelers are limited to the island residents who however are not many, since Sardinia doesn't have a very large population.
I recommend Santa Teresa. Other bigger towns in the area are Palau, which is also an easy boat trip to the Maddalena Archipelago. Alghero is also nice, a bit bigger. Olbia proper is not my favorite (it's the largest port town in Northern Sardinia), but there are nice areas not too far away (including the Costa Smeralda, which however is pricey).
You will need a rental car for the island. I presume you are aware of that. Be also aware that the island is very large and roads are curvy so it takes more time than expected to get from point A to point B.