My son twice dropped to 34cwhen he was about 12-18 months (he is 12 now so can't remember exactly).
He had been poorly, fever etc. I'd given calpol and then he went cold, he was cold to the touch. It was scary, I called 111 and they actually sent an ambulance. Meanwhile I had been cuddling close with blankets etc.
By the time we were seen I. The hospital (had to wait a bit when got there as obviously not top priority) his temp had returned to normal.
The doctors and nurses did t explain and seemed pretty shrug about it while insisting on getting a pee sample from him so had to wait around for ages with nappy off per pot at the ready...
Anyway, that is all beside the point, sorry. I eventually got a dr to explain that what can happen when small children's bodies are trying to regulate their temperature against fever sometimes the internal thermostat over compensates and they go too far the other way.
It did happen to him once more a few months later, lots of body heat and blankets and he came back to normal.
This factor, combined with recent medical advice (from dr xand on bbc) that fever is the body's tool for fighting infection and shouldn't be brought down for its own sake unless way too high, means that I don't medicate my younger kids for fever.
It is alarming and not something that is spoken about much. Hope your little one warms up and feels better soon.