Observations of high-redshift quasars at z ≳6 imply that supermassive black holes (SMBHs) with masses were in place less than 1 Gyr after the big bang. If these SMBHs assembled from ‘seed’ BHs left behind by the first stars, then they must have accreted gas at close to the Eddington limit during a large fraction (>rsim 50 per cent) of the time. A generic problem with this scenario, however, is that the mass density in M ∼ 106 M⊙ SMBHs at z ∼ 6 already exceeds the locally observed SMBH mass density by several orders of magnitude; in order to avoid this overproduction, BH seed formation and growth must become significantly less efficient in less massive protogalaxies through some form of feedback, while proceeding unabated in the most massive galaxies that formed first. Using Monte Carlo realizations of the merger and growth history of BHs, we show that X-rays from the earliest accreting BHs can provide such a feedback mechanism, on a global scale. Our calculations paint a self-consistent picture of BH-made climate change, in which the first miniquasars – among them the ancestors of the z ∼ 6 quasar SMBHs – globally warm the intergalactic medium and suppress the formation and growth of subsequent generations of BHs. We present two specific models with global miniquasar feedback that provide excellent agreement with recent estimates of the z = 6 SMBH mass function. For each of these models, we estimate the rate of BH mergers at z > 6 that could be detected by the proposed gravitational-wave observatory eLISA/NGO.