Rinse trout and pat dry. In a small bowl, mix sugar, salt, lemon peel, and thyme; rub evenly over flesh sides of fish. Stack trout in a 9- by 13-inch baking dish. Cover and chill to cure at least 1 hour or up to 3 hours.
In a bowl, soak wood chips in 2 quarts of water for 30 minutes.
Drain.
If using a charcoal grill, ignite 60 charcoal briquets on firegrate. When dotted with gray ash, in 20 to 25 minutes, push half the coals to each side of grate.
Sprinkle half the wet wood chips on each mound of coals. Position grill about 6 inches above grate.
If using a gas grill, turn heat to high. Put wet wood chips in smoke box or foil pan directly on heat. Close lid and heat for about 10 minutes. Adjust heat for indirect grilling (no heat down the center).
Rinse fish well and pat dry. Coat skin sides of fish with oil and lay fish, skin down, on grill, not over heat source. Cover barbecue; open vents for charcoal. Cook until fish are opaque but still moist-looking in center of thickest part (cut to test), 8 to 10 minutes. With a wide spatula, transfer fish to a platter.
