We study the thermopower and some related transport quantities due to the orbital Kondo effect in a single quantum dot system with a finite value of Coulomb repulsion by means of the noncrossing approximation applied to the multiorbital impurity Anderson model. It is elucidated how the asymmetry of the renormalized tunneling resonance due to the two-orbital Kondo effect causes characteristic behavior of the thermopower at finite temperatures under gate-voltage and magnetic-field control, which is compared with that of the ordinary spin Kondo effect.