Preheat the oven to 350 degrees F.
In a small bowl, mix together the mayonnaise, olive oil, cayenne, salt and some pepper.
Peel back the corn husks, leaving them attached at the base, and remove the silks. Brush the kernels with the mayonnaise mixture, then replace the husks. Place the ears on a baking sheet and roast for 20 to 25 minutes, rotating the corn halfway through.
Remove to a platter and cut off the husks. Squeeze lime juice over the corn, and then sprinkle with the Cojita and cilantro. Serve warm.