Is it safe to use an old mobile phone as modem / router for Wifi?

(Related to A phone as a home 4G modem/router?)

I was wondering if it is plausible and safe to keep an old phone charging all the time with a sim card in order to use it as a modem/router for Wifi.

I thought about this idea in order to have a low-cost Wifi for an alarm system. However, my mother is afraid the mobile phone, if left all day charging and running, might explode and start a fire. Is it possible this would happen?