Upon heat shock, the fission yeast Hsp40 chaperone Mas5 drives temperature-sensitive proteins toward protein aggregate centers (PACs) to avoid their degradation until lower temperatures favor their refolding. We show here that cells lacking Mas5 are resistant to oxidative stress. Components of the general stress pathways, the MAP kinase Sty1 and the transcription factor Atf1, are suppressors of this phenotype. Strain  Δmas5  expresses higher levels of Sty1- and Atf1-dependent stress genes than wild-type cells. Pyp1, the main tyrosine phosphatase maintaining Sty1 inactive in the absence of stress, is a temperature-sensitive protein that aggregates upon temperature up-shifts in a Mas5-dependent manner. In strain  Δmas5,  Pyp1 is sent to proteasomal degradation even in the absence of stress. We propose that Pyp1 is a thermo-sensitive phosphatase, which during heat stress coalescences into PACs in a Mas5-dependent manner, to promote full activation of the anti-stress Sty1-Atf1 cascade.