Whether the plastic piece is there or not doesn't make a difference, I personally wouldn't use it because its just another piece of something that can be dislodged and mess with the probe placement. You want to make sure that the probe is completely covered by tape also.

As far telling how hot it is without a thermometer thats kinda hard. Assuming our body temps are 98.6 if you touched the hotspot is shouldn't feel hot but slightly warm.

Do you have to house snakes in this rack right now? If not I would just sit tight until the temp gun came in.