Morning.... First.... food should always be cooked from start to finish in one process... Bacteria has started to grow as the food warms up, and needs to be killed with the final cooking temp in the proper length of time.... If the bacteria was not killed before the process was completed, it remains growing during the cooling down process until the IT of the meat has reached ~40 degs. F... As you reheat it to get to final killing temp., the bacteria starts growing again until the final temp. kills it....
That's the text book answer....
Scientifically speaking..... There is what's called a "Pasteurization Table"... The table below shows the time and temperature required for a 5 log reduction to make meats safe... holding longer at those temps just kills more pathogens... The temps listed are Internal Temps of the meat product... Very important all sausages were up to the IT.... You will have to judge what happened in your process.....
I would submerge the sausage in a water bath at 165 deg. F until the IT reached 160.... Just to be on the safe side... and hold there for 2-3 minutes....
FSIS Guidance on Safe Cooking of Non-Intact Meat Chops, Roasts, and Steaks April 2009
Temp °F / Time for 5.0 log Reduction
Unit Time
130.......... .86 min.
131 ...........69 min.
132.......... 55 min.
133.......... 44 min.
134............ 35 min.
135............. 28 min.
136 ..............22 min.
137 ...............18 min.
138 ...............14 min.
139............... 11 min.
140 ..............9 min.
141.............. 7 min.
142 .............6 min.
143 .............5 min.
144 .............4 min.
145 .............3 min.
146 ..............130 sec.
147.............. 103 sec.
148 ..............82 sec.
149 ..............65 sec.
150............... 52 sec.
151................ 41 sec.
152................ 33 sec.
153 ................26 sec.
154 ................21 sec.
155 ................17 sec.
156 .................14 sec.
157 ..................11 sec.
158 ...................0 sec.
159 ....................0 sec.
160 ....................0 sec.
The required lethalities are achieved instantly when the internal temperature of a cooked meat product reaches 158 °F or above. Humidity must be considered when using this Time/Temperature table.
This Time/Temperature table is based on Thermal Death Curve for Salmonella in Beef Emulsions in tubes (Derived from Goodfellow & Brown1, 1978) Regulatory Curve obtained from Jerry Carosella, Deputy Director, Microbiology Division, Science and Technology. All times that were a fraction of a minute or second was rounded up to the next whole number (e.g., 16.2 seconds for 155 °F was round up to 17 seconds).
________________________ 1. Goodfellow, S. J. and W. L. Brown. 1978. Fate of Salmonella Inoculated into Beef for Cooking. Journal of Food Protection. 41:598-605.