How to switch on 32A/240VAC with Arduino?
I don't want to try anything that results in a fire hazard.


That's a good idea. 

Besides those toy relays there are real ones:
440 V AC * 63 A (Around there, you can find smaller ones too)

BTW: Don't rely on what's printed on the relay itself, with cheap Arduino relay modules. 230V and some current need proper handling by the PCB board as well (size and distance of the copper tracks on the scondary side)

If you want a solution that could be certified (or certifiable) as "safe" there probably won't be an Arduino involved or being built by anyone asking questions like you do  ;(   (sorry)