DO NOT DO WHAT YOU PROPOSE!!
I caution you for two reasons.
First, most products are intended to be used with a supply voltage no more than 10% over the nameplate voltage. You propose to exceed this.
Secondly, such systems are to be GFCI protected. Your GFCI would be the breaker supplying the tramsformer- and I fear the transformer will prevent it from protecting the circuit. Should you place it after the transformer, you will be exceeding the voltage it is designed for as well.
You'ld be better served by installing a recessed light in the ceiling, with a heat lamp bulb shining on the floor- assuming, of course, that this is outside the shower area!
