woodburning stove enclosure, Thermalite blocks

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Hi, the builder is part way through building a inglenook fireplace onto an external wall, to house a wood burning stove. The back inner wall has been built with Thermalite blocks and the external wall with brick. I had a Hetas installer come around to quote for installing the stove etc He said that he wasn't sure if Thermalite blocks were acceptable, as they're liable to crack with the heat. The enclosure will be lined with cement boards and above the enclosure will be brick chimney, lined with pumise chimney blocks. Does he need to knock it down and start again?

Thanks