Heat shock transcription factor 1 (HSF1) has been identified as a therapeutic target for pharmacological treatment of multiple myeloma (MM). However, direct therapeutic targeting of HSF1 function seems to be difficult due to the shortage of clinically suitable pharmacological inhibitors. We utilized the Ugi multicomponent reaction to create a small but smart library of α-acyl aminocarboxamides and evaluated their ability to suppress heat shock response (HSR) in MM cells. Using the INA-6 cell line as the MM model and the strictly HSF1-dependent HSP72 induction as a HSR model, we identified potential HSF1 inhibitors. Mass spectrometry-based affinity capture experiments with biotin-linked derivatives revealed a number of target proteins and complexes, which exhibit an armadillo domain. Also, four members of the tumor-promoting and HSF1-associated phosphatidylinositol 3-kinase-related kinase (PIKK) family were identified. The antitumor activity was evaluated, showing that treatment with the anti-HSF1 compounds strongly induced apoptotic cell death in MM cells.