How use DMM thermocouple probe hands-free to monitor heatsink temperature?
Best way I think is thermal compound and glue it to the device, then just buy another thermal probe :)   Short of that you can try and tape or clamp the flexible wire, I've had luck using a binder clip or some locking pliers like vice grips.  Then curve it so the bend in the wire provides natural holding force onto the heat sink.   That way what you're using to hold the probe doesn't affect the measurement.  But really glue is the way to go.

For more pro use you can use thermal loggers that use slightly cheaper thermal couples, there are some nice ones that help you measure air flow at the same time.

That said for another project I just built a little wind tunnel and started using the bent wire approach so it's up to you how accurate you need to be.