We investigate the production of mesons, baryons and exotic tetraquarks containing heavy flavors, $b$ and $c$, in the framework of coalescence quark model. The Wigner function for the produced cluster is defined in terms of wave functions calculated from exact solutions of the few-body problem using a realistic constituent quark model. It contains a chromoelectric part made of a Coulomb-plus-linear interaction together with a chromomagnetic spin-spin term described by a regularized Breit-Fermi interaction with a smearing parameter that depends on the reduced mass of the interacting quarks. We take into account effects of temperature on the masses of the light quarks that enter in the constituent quark model. The temperature dependence of those quantities are taken from the Nambu--Jona-Lasinio model. We use such formulas to calculate the yields for $\bar{D}^{0}$, $\Lambda^{+}_{c}$, $\Xi^{++}_{cc}$, $T_{cc}$ and $T_{bc}$. We find an enhancement in the number of all clusters produced when temperature effects are taken into account. We also find that the color component $6\bar{6}$ of the overlap between the Wigner function of the produced hadron with the phase-space distribution of the constituents at finite temperatures is strongly suppressed for $T_{cc}$ and $T_{bc}$ tetraquarks.