Could I please have an example of a everday experience of a chemical process for which a rate increases with temperature? I thought of ice melting but its a physical change...

One example is the burning of a candle. The wax, which is a hydrocarbon, doesn't burn at room temperature because the reaction to form CO2 and H2O is so slow. But heated up with a match (which overcomes the activation energy), the reaction is exothomeric and produces enough heat to keep the ocmbustion going. Same thing with burning wood in a fireplace. The wood/oxygen reaction is so slow that we store wood on a rack outside or inside near the fireplace. But a match gets things going. Finally, as a third example, the rusting of iron is a slow process but rusting takes place faster at an elevated temperature.