Within the framework of constituent quark model, it is shown that single hadron fragmentation functions of a parton can be expressed as a convolution of shower diquark or triquark distribution functions and quark recombination probability if the interference between amplitudes of quark recombination with different momenta is neglected. The recombination probability is determined by the hadron's wavefunction in the constituent quark model. The shower diquark or triquark distribution functions of a fragmenting parton jet are defined in terms of overlapping matrices of constituent quarks and parton field operators, similarly as dihadron or trihadron fragmentation functions in terms of parton operator and hadron states. Extending the formalism to the field theory at finite temperature, we automatically derive contributions to the effective single hadron fragmentation functions from the recombination of shower quarks with thermal constituent quarks. Such contributions involve single or ...