Pat the shrimp dry, then toss with the olive oil, thyme, smoked paprika, salt and pepper on a large rimmed baking sheet. Arrange in a single layer and roast until just cooked through, 8 to 10 minutes.
Roast, stirring halfway through ... Transfer the diablo sauce to a large bowl, add the shrimp, mix until well coated. Chill and marinate the shrimp for at least 10 minutes, or up to 1 hour.