With Chinese and I assume Carolina as well temperatures below optimal (80) will at worse mildly stunt your mantis's growth/molting schedule.
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Room temperature (72-75 F - 22-24 C) is preferred for those two species, and is more optimal for them (spring season weather). See the caresheet on
general care,
Chinese mantis here,
also here, and
Carolina mantis to name just a few.
If you are keeping them at warmer temps of 80F (27 C) or higher they obviously do molt faster due to a increased metabolism from the extra heat, which shortens their lifespan. They do survive in nature in higher temperatures too during the summer; however the night's cool off period (and seasonal weather changes) provides a balance, and is not that warm for their entire life (unlike captive kept).
I'd suggest you to stop using heaters with those species. I know though everyone tends to find a care "groove" and sticks with it.
We're going out of town for a few days and I'll have only been a mantis owner for a little over a week. I'm a little nervous to leave her home by herself.
I'm guessing since we'll only be gone for three days that the best thing to do would be to feed her before we go and just leave her home, but...I still want to ask, do you take your mantids on vacation with you? We'll be in a hotel room, so humidity and temperatures won't be ideal for her, but asking anyway. And if you do travel with them, how do they take to being in their container in a moving vehicle? Is that too stressful?
Yes, at a week without feeding they can develop a lethargic condition that can shorten mantids lifespans or lead directly to their death (Praying Mantis Ultimate Care Guide, book page 89 so no link). I've had it happen myself for various reasons my few mantids went without food for a week and there were three types of outcome - dead, skinny and did not recover, and a few that were fine. It seems males fared better, such as a similar event even if offered feeders daily can go a few weeks without food just fine (as adults ready for mating).
Ideally you would have a friend or neighbor care and feed for your mantids during your vacation or absence.
While mantids can survive being shipped in the mail which is said to be one of the worse things for it, it also provides a better result as the box and insulation often protects it from sudden temperature changes. If you are taking a mantid from a cold/hot car or house to another environment it does stress the mantid and can lead to health issues, the bigger the temperature change is, the bigger chance for a bad outcome.
I will just warn you to keep your mantids out of direct sunlight in a container.
I found out first hand collecting some wild mantids and placing them in individual containers in the shade. After more were collected the sun moved and caused a few to be exposed to direct sunlight for not even five minutes and all of them were dead when I returned with another mantid.
I also will likely be taking her (a Carolina) to a classroom that's about an hour away in a couple of months, provided she's up for it. I wouldn't plan on taking her out of the container in the classroom (I'm guessing too many active students might freak her out and make her move too much), but I wouldn't mind knowing if this is something anyone has done before and how the mantids have handled the experience.
No problem there I've traveled further with mantids I captured to return home. I would only suggest arriving early so the mantids have at least 15-30 minutes to return to a less stressful state from the trip before the classroom event. Otherwise if you planned any hands on activities or such you may encounter issues with aggression from the stress.
How about heat? Do they handle outside temps well if not in the direct sunlight and getting heated up in their enclosure?
Covered in the information above. If it is a gradual temperature change the mantid will be fine; however, sudden temperature changes of more than 20 degrees F can lead to health problems or it's death.
They however handle outside temps fine, as they are a native species.
Wild mantids though are raised in that environment and the temperatures raise/fall gradually with the mantid expose to it the whole time, so it will not experience sudden temperature changes like a captive mantid pet will being introduce to the outdoor temperatures.