Styrene boils at 145C and decomposes into gas at 280C. So at 300C it is decomposed. Unless you synthetize Sty by yourself , it always has some inhibitor if you bought or even purify. Moreover depending on your way of acquisition , oxygen could be there or light could be an initiator
so if you question is pure science - mathematic then the you got the first 2 numbers of tenperature
if you want to do in the lab then you should have all the chemical precaution in order to do it safely and accurately to generate scientific data
Styrene is a highly reactive compound that polymerizes and oxidizes easily. The polymerization reaction, which is slow at room temperature, is accelerated by the action of light, heat (especially above 66°C), or chemical agents (peroxides, strong acids, metal salts, etc.).
Is 300 a fixed parameter ? Temperature selection in any scaleup process is based upon the residual time of the reaction mixture in that heating zone, so that materials do not degrade. If you can maintain the flow and temperature, it may be possible even at 300. It is like having a flash, and can be performed in very small scale with due safety to check the outcome.