Are you sure that you need a backflow temperature for an inlet boundary condition?
Backflow temperature usually is required for an outlet or pressure boundary condition for the case, that fluid enters into the computational domain from the outside due to reversed flow. In general you should strive to specify boundary conditions such, that no reversed flow occurs on that boundary patch. This is mainly because in such a case fluid with an unknown state and properties would enter the domain. All what you can specify for this situation is just a guess about what potential state that fluid might have, which enters the domain by reversed flow on e.g. an outflow boundary. It is a large source of uncertainty. Usually some blind guessed value (e.g. ambient temperature) is specified. If you do not know anything else, you can specify the same temperature value what you would assume close to that boundary inside the computational domain.
Not necessarily. If the boundary condition is placed such that it cuts a recirculation vortex, than mesh refinement will not help. Please have a closer look on how your predicted flow field looks like.