"Red" brick really doesn't tell us anything.
A red brick could be cement brick (big no no), a solid waterstruck brick (maybe OK), a modern face brick (cored or not), or a fire brick of some sort (preferable; usually not red, but some are colored).
Each of these types has a different suitability for cycled heat work, so the color may not be a good indicator. Tscarborough's answer is right.
As a side note- there are cream colored common brick in Australia that will stand incredible heat- they are effectively fire brick, and many a high temp pottery kiln has been built of them.