We don't feel heat from objects that have been heated up but aren't close enough to touch primarily because heat is transferred through three main mechanisms: conduction, convection, and radiation.
Conduction: This is the transfer of heat through direct contact between two objects. When objects are in direct contact, heat energy can transfer from the hotter object to the cooler one. For example, if you touch a hot pan, heat is conducted from the pan to your hand.
Convection: This mechanism involves the transfer of heat through the movement of fluids (liquids or gases). When a fluid is heated, it becomes less dense and rises, allowing cooler fluid to take its place. This creates a convection current that transfers heat. For example, when you boil water, the heat from the stove is transferred to the water through convection.
Radiation: Radiation is the transfer of heat through electromagnetic waves. Unlike conduction and convection, radiation does not require direct contact or a medium for heat transfer. All objects above absolute zero temperature emit thermal radiation. This radiation can travel through space and be absorbed by other objects, including our bodies. The transfer of heat from the Sun to the Earth is an example of radiation.
In the scenario you mentioned, where objects are heated up but not in direct contact with you, the heat transfer mechanism would most likely be radiation. If the objects are not emitting significant thermal radiation or if the radiation is not being absorbed by your body, you would not feel the heat. This is because the amount of heat being radiated and absorbed is relatively low or negligible compared to other sources of heat in your environment.
It's important to note that while you may not feel the heat directly, radiation can still impact the overall temperature of a space. For example, standing near a hot stove, even without touching it, can increase the temperature in the surrounding area due to the radiation emitted by the stove.