A couple of things will need to happen, They'll have to win at least 30 games straight in order to put it on the forefront of their mind to make "history". The coaches and management team as well as the players would have to be on the same page with regard to making it a priority.
I remember when the Chicago Bulls went 72-10. That team (wanted) to win every single game night in and night out. They were shooting for perfection. In today's climate it is more like what cdpayne described: If they lock up the best record to have home court for the whole playoffs they are likely to rest their stars. If on the other hand OKC and San Antonio keeps the pressure on them by staying within a couple of games for the best record for the remainder of the season then Miami will have an incentive to keep putting their best efforts out there. Last but not least they have to stay healthy. At any moment a key player could get injured.