[anonymized]:

Perhaps trying a TC in the coffee cake once or twice and correlating that with your exit temperatures will provide a way to approximate. Then you won't need to ruin shots to measure.

I'm suggesting the thermocouple measure the coffee cake during the extraction. I got fancy and hooked mine to a data logger and to Artisan software. The Artisan tracing can then be magnified so you see the temperature in the coffee cake during the course of the pull. Here's how I did it. It's not the only way but it works.

The temperature profile of a commercial lever group

You can avoid sacrificing a basket by threading a thin thermocouple into the top of the basket and locking in. Pretty soon your insulation on the thermocouple wears out, though.

[anonymized]:

If the probe is not in the coffee cake itself I think the temperature measurement will be low. With the probe below the basket the water has had a chance to be cooled by the coffee and the rest of the brewing chamber. By inserting the probe in the coffee cake I found the extraction was still relatively undisturbed so I was able to taste it.

Very nice! Can you provide photos of that too?