A machine system includes a compressor, and a cooler having an inlet tank to receive compressed air from the compressor, and a header assembly attached to the inlet tank and including a plurality of cooling tubes supported in the header and each having an external heat exchange surface exposed to a flow of cooling air. The cooler further includes a plurality of graphite pack seals each extending peripherally around one of the cooling tubes, and a clamping assembly clamping the pack seals against the header to squeeze the pack seals into sealing contact with the cooling tubes and the header.