In MMIC devices, N/C means nothing is connected to them inside. This means you can connect them anywhere without an effect on device performance.
I would test the N/C connect or not-connect before I finish my design. Although the tabs are tiny, they may affect device response at the upper frequency end.
In TTL and similar circuits, however, the rule is "connect unused gate inputs to +Vcc". I had a terrible problem with TTL gates made by National where the data sheet read" connect unused gate inputs to +Vcc or to GND". My colleague dared to connect them to GND upon which devices literally exploded. National technical service never responded.
I agree w/ IanP. If the N/C pin is connected to some test circuit that is only used during wafer fabrication post-testing, then connecting it to ground could make the device perform incorrectly (or maybe draw excess current through a circuit that is normally left isolated).
If it says No Connect, then don't connect to it.
As for heatsinking... it may help a little, but most of your heat flow should be through the bottom of the part. This is generally why MMIC power amps and the like have requirements for Au/Sn eutectic bonding; to get the heat out of them through the largest surface that is in closest physical proximity to the heat-generating part of the MMIC.
Some manufacturers use some pins for migrations. When designing for device migration these pins may be connected to power, ground, or a signal trace depending on the pin assignment of the devices selected for migration. However, if device migration is not a concern leave these pins floating. In your case leave them alone. If you connect them to gnd this will be just heat sink nothing else, but I recommend that you do not drive any signals into this pins. In some cases this N/C have internal connections and manufacturer say leave them floating/without connection to anything. Do all according to datasheets no experiments, do not be electronics cowboy. ;-)