This is completely different than what Catholics believe in as purgatory. The present heaven has nothing to do with punishment or suffering. The present is not somewhere between heaven and hell. It is the duration of time between the present life and the future ultimate heaven after the resurrection. It doesn't mean half way between heaven and hell but where we are in between. The intermediate heaven is the common theological term for where we go as Christians when we die and where we stay until the return of Christ and the resurrection.
For more information on the subject of Heaven, see Randy Alcorn’s book Heaven.