A block style heat exchanger for a heat pipe reactor having a plurality of heat pipes extending from a reactor core. The heat exchanger includes a plurality of primary channels, each for receiving heat transferred from the core via one of the heat pipes. The primary channels extending within a block of one or more materials. The heat exchanger also includes a plurality of secondary channels defined within the block for transmitting a flow of the secondary heat transfer medium through the heat exchanger from an inlet to an outlet. The block is formed from one or both of: a plurality of plates bonded together, with each plate defining at least a portion of one or more of the plurality of primary channels and/or the plurality of secondary channels, and/or a unitary piece of material formed from an additive manufacturing process.