Normally I would take the vacuum with a longer extension and brush attachment and vacuum off the evaporator going up through the inside of the AC filter area. The problem with this is you can only get a portion of the total area due to access.
Last year I had to replace the blower motor on my front AC unit.
Since I had to have the sheet metal off of the front air handling compartment that holds the evaporator I took the time to blow it out from in the reverse direction the air normally flows. I removed the filter and put some rags up there to catch any of the dirt. It seemed to have total air flow but it did lower the temp of the air coming out which was warmer then the rear AC.
I have a hand held thermo gun that I bought at Harbor Freight, I use it to check axle hub, brakes, tires temperature while on the road.
2002 Monaco Windsor 38 PKD
2005 Jeep Grand Cherokee w/5.7 Hemi