OK, digging into the rules on page 211 of the current version of Campaign Operations:
"Each item involved in the refit, whether being added, moved or removed, requires exactly one instance of its standard replacement time (see pp. 205-207)."
The good news is page 205 says Heat Sinks are replaced "per location; treat Engine as 1 location". The bad news is IS DHS don't fit in legs, so if you had any of your 17 SHS (for purposes of this example) there, they would have to move, and that kicks the refit up to Class C. For simplicity's sake, we'll assume there are 12 SHS in the engine, 2 in one side torso, and 3 in the other.
Per page 205, you need to remove three locations worth of SHS, then install three locations worth of DHS. A location of Heat Sinks takes 90 minutes (before the refit class multiplier, which is 3 for Class B), so 270 for each location, each time. So the work could look like:
Remove SHS from one side torso (270 minutes)
Remove SHS from other side torso (270 minutes)
Remove SHS from the engine (270 minutes)
Install DHS in the engine (270 minutes)
Install DHS in one side torso (270 minutes)
Install DHS in other side torso (270 minutes)
Doing it that way would mean you'd get the DHS in the engine online in 18 hours (if you don't rush it), and the rest after a further 9. If you try installing any DHS before removing all the SHS, I'd go with Sartris' suggestion, i.e., nothing works until you're in a condition where there's only one type of HS.
Rush jobs and throwing extra bodies at work are possible, but interact in not exactly the same way:
Up to two extra teams can be assigned to a particular unit, each one giving you a bonus of 1. The extra teams can be no more than one experience level below the lead team.
Rushing halves the time required per experience level reduction of the lead team. If you start with an Elite team, this translates to a 2 penalty for the first reduction (meaning throwing two additional teams at it will mean no penalty). Reducing a second time is another 1 penalty, but means only a quarter of the time is necessary. Reducing three times (the maximum) is another 2 penalty, but gets the time required down to 1/8th of the original.
The good news is that Heat Sink replacement is easy, with a target number reduced by 2, so your Elite team with two extra teams helping would succeed on a 4 or better in just under three and a half hours, or 34 minutes for each step.