I drove around for a few weeks this summer w/ no front axle or 1/2 shafts.

Had the same concerns with grease/bearing contamination.

I used an inside caliper to measure the diameter of the area where a temp cover would reside, then used a compass (circle drawing thingy) to mark the proper size disc on a plastic coffee can lid. (I prefer Folgers...Black Silk)

Then cut said disks, & pushed them into place from the back side.

They held up just fine, with no sign of distortion from heat....