“autoGrow” is part of the answer — it corresponds to “Exactly xx mm” in the interface. The other part is, well, actually changing the row height. Fortunately, ID allows all kinds of shortcuts. If you find your specified text and its 'parent' (i.o.w., the containing element) is a cell, you can immediately set the new row height into that. ID is smart enough not to try and apply this on just a single cell.
Putting it together into a javascript:
app.findTextPreferences = null;
app.findTextPreferences.findWhat = “Specified text”;
results = app.activeDocument.findText();
for (a=0; a<results.length; a++)
if (results[a].parent instanceof Cell)
results[a].parent.properties = {autoGrow:false, height:”8.25mm”};
(Note: sometimes this editor changes straight quotes to curlies. JS only accepts straight quotes — change where necessary!)