As Jim Breeyear stated, the heater should shut off automatically if
the air is interrupted (or get a pressure/flow sensor to
shut it off if it doesn't!).
The heat in the probe will build up a bit (now the heater is off,
but still hot & heating up static air - the temp might go up 5 to 10
degrees before it starts going down. Try for yourself to see what
happens to temp. when the air is shut off (if you're nervous,
keep one hand on the flow control!)
Better yet,
Instead of worrying whether the temp change will affect the probe
or sample and probably ruin the experiment, why not have a standby -
a tank of air, or a high pressure liquid N2 dewar (just don't
do a fill from that tank!) attached to the line
ready to kick in when compressor fails? The cost would be
a regulator, couple of check valves, assorted plumbing, gas and
tank rental and space to put the tank.