  In this paper, we study the gravitational collapse of a fluid ball undergoing
dissipation in the form of heat flux, in the framework of $f(R,T)$ gravity. To
apply the junction conditions in order to match the interior and the exterior
spacetimes and analyze the dynamics of collapse, it is necessary to know the
exterior metric for the radiating fireball, which is not yet available in the
context of $f(R,T)$ gravity. Therefore, at the outset, we have determined the
exterior Vaidya-like radiating metric in $f(R,T)$ gravity. Subsequently, we
solved the $f(R,T)$ field equations and used the $f(R,T)$ junction conditions
to match the exterior with the interior spacetime. The time of formation of the
singularity and the time of formation of the apparent horizon have been
determined. It is concluded that the final singularity is hidden behind the
horizon.
