We study the nature of the finite-temperature chiral transition in QCD with N-f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi(4) theory with a complex 2N(f) x 2N(f) symmetric matrix field and symmetry-breaking pattern SU(2N(f)) --> SO(2N(f)). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without c expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4) --> SO(4). This fixed point does not appear in an c-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.