We derive constraints on feedback by active galactic nuclei (AGN) by setting limits on their thermal Sunyaev-Zel'dovich (SZ) imprint on the cosmic microwave background. The amplitude of any SZ signature is small and degenerate with the poorly known sub-mm spectral energy distribution of the AGN host galaxy and other unresolved dusty sources along the line of sight. Here we break this degeneracy by combining microwave and sub-mm data from $Planck$ with all-sky far-infrared maps from the AKARI satellite. We first test our measurement pipeline using the Sloan Digital Sky Survey (SDSS) redMaPPer catalogue of galaxy clusters, finding a highly significant detection (>20$\sigma$) of the SZ effect together with correlated dust emission. We then constrain the SZ signal associated with spectroscopically confirmed quasi-stellar objects (QSOs) from SDSS data release 7 (DR7) and the Baryon Oscillation Spectroscopic Survey (BOSS) DR12. We obtain a low-significance (1.6$\sigma$) hint of an SZ signal, pointing towards a mean thermal energy of $\simeq$5\times 10$^{60}$ erg, lower than reported in some previous studies. A comparison of our results with high-resolution hydrodynamical simulations including AGN feedback suggests QSO host masses of $M200c$ ~ 4 × 10$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}h-1$M$\odot$, but with a large uncertainty. Our analysis provides no conclusive evidence for an SZ signal specifically associated with AGN feedback.