The present invention relates to a composition for dyeing keratin fibers, comprising at least (i) one or more copolymers derived from the polymerization of at least one crotonic acid monomer or crotonic acid derivative and of at least two different vinyl ester monomers, (ii) one or more thickening polymers bearing (meth)acrylic acid unit(s), and (iii) one or more pigments. The invention also relates to a dyeing process in which said composition is applied to keratin fibers, the operation optionally being followed by drying. The composition makes it possible to obtain temporary dyeing having the advantage of forming a transfer-resistant deposit, leaving the treated fibers individualized, with an improved cosmetic feel.