A certain object with a surface temperature of 150 degree C is radiating heat at a rate of 200 J/s. To triple the object's rate of radiation energy, what should be its surface temperature in Celsius?

150 C is 423 K.

Because of the Stefan-Boltzmann law, which you should learn, the total emission at all wavelengths is proportional to T^4. Absolute temperature must be used.

To triple the emission, T has to increase by a factor (3)^1/4 = 1.316

That makes the required absolute temperature 557 K.

Convert that to Celsius.