We have radiant heat floors under marble in our bathroom and I need a non-slip bath mat. Please don't tell me to put a towel down - that towel can scoot out from under your feet and cause falls. I've read that diatemaceous earth bath mats are good for heated floors as the heat conducts. But they require a non-slip mat underneath. An open weave mat should be ok but is natural rubber ok to use? Silicone? Don't want it to melt to floors. The highest we set it is 80 degrees.