The Hurricanes cruised past the Heat's 6-145 just one wicket down and with more than five overs to spare at Bellerive Oval on Tuesday to go two wins clear atop the table.
Short smashed 68 from 41 balls in a 132-run partnership with rookie Caleb Jewell, who kept pace with 61 not out from 38 balls.
None of the Heat bowlers escaped punishment against the pair, who were measured after the early loss of Matthew Wade before unleashing in the middle overs.
Earlier, Archer took a boundary blinder and two wickets in two balls as the Heat collapsed to 4-27 inside the first six overs.
Archer (2-28 from four overs) backed it up with the big wicket of Chris Lynn and Matthew Renshaw two overs later.
Alex Ross and Heat skipper Jimmy Peirson (50 from 48 balls) salvaged the innings with a 109-run fifth-wicket partnership but it wasn't enough.
Ross clobbered eight fours on his way to 62 from 35 balls under a thick cover of smoke in Hobart from bushfires burning southwest of the capital.
The Heat remain in second last with just three wins from 11 matches.