The thermal vibration and buckling behavior of a functionally graded nanoplate are examined in this study. The nanoplate is made up of a silicon nitride/stainless steel core plate and two cobalt-ferrite/barium-titanate face plates. Four alternative porosity models were used to simulate the porosity of the nanoplate, and numerous variables that can affect the nanoplate’s behavior were taken into account. The study found that the thermomechanical behavior of nanoplates with magneto-electro-elastic face layers and a functionally graded porous core plate is affected by material gradation indices, porosity ratios, nonlocal variables, and different core plate material porosity models.