Going along with the above folks and keeping the door closed to keep the kittens out, you can get a little spring thing that attaches to the door hinges and will automatically close the door for you. Even if it doesn't latch, it does close and I think it would be beyond the abilities of a kitten to push open.

Alternative idea might be to hang a hook from the ceiling/wall (small screw in kind like you might use to hang a stocking off of a wood fireplace) and hang the lamp from it (some sort of rope or small chain perhaps) slightly raised above the cage. If you can re-calibrate temps with the lamp slightly elevated, hanging means it can't be knocked over onto things that might burn and as long as there's nothing for a kitten to push underneath it that might burn, that should eliminate any accidents from the lamp being moved. If it swings a little, it should be fine even if it touches anything for a few seconds. Gravity will bring it back to the "safe" position where it isn't touching something.

I haven't had snakes too long and so far haven't had to set up a lamp heater, but hanging sounds to me more stable to prevent any accidents than even a lamp stand. As long as what it hangs from can't be knocked out, it wouldn't be able to fall.

Perhaps the most secure method to hang I can think of would be a combo of these 3 things for the cheapest method:
1 of something like this (can't tell if the hole is big enough online, I'd make sure to look in store): https://www.homedepot.com/p/Everbilt...6916/204273856
2 of these to attach the chain to the screw and the chain to the lamp: https://www.homedepot.com/p/Everbilt...2704/205887774
However much of this to hang it: https://www.homedepot.com/p/Everbilt...0016/204640736