Question: How do we sense (feel) temperature?
Our skin has temperature sensors all over it. We only feel hot or cold when the temperature of these sensors is changed by heat flowing into or out of our skin. So what we actually feel is not the temperature of the ice cube, only that heat has been transferred from our skin causing our temperature sensors to tell our brain that the temperature of our skin has become lower. Our brains interpret this information as being about the temperature of the ice cube. We can also judge the degree of hot or cold indirectly by the rate at which the temperature of our skin changes.
Hopefully you notice that we have made little use of the word temperature so far. That was deliberate. Please try to keep Heat and temperature separate in your heads! Time to talk about temperature.