Preheat the oven to 375°F.
In a large, oven-safe saute pan, heat the oil over medium-high heat. Place the hake in the hot oil, presentation side down. Cook for 2 minutes, then lower the heat. Add the butter to the pan and let it brown around the fish for 3 to 4 minutes. Remove the pan from the heat and carefully flip the fish over. Transfer the saute pan to the oven and bake for 5 minutes.
Remove the fish fillets to a serving platter. Brush the fillets with the lemon juice and garnish with thyme leaves. Season with salt and white pepper.