Balancing higher engine efficiency with safety and operational concerns involves a multi-faceted approach. Engineers often have to make trade-offs between efficiency, safety, and longevity of the engine. Implementing advanced cooling systems, using materials that can withstand higher temperatures, and employing predictive maintenance strategies to identify potential issues before they occur, are common practices. Additionally, regulations and standards are in place to ensure that efforts to increase efficiency do not compromise safety. Innovations in material science, engineering design, and operational protocols are continuously sought to push the boundaries of these limitations safely and effectively.

The temperature difference between the hot and cold reservoirs is a critical factor in the efficiency of a Carnot engine. A larger temperature difference increases the efficiency, as per the formula ηCarnot = 1 - (Tc / Th). As Th increases or Tc decreases, the efficiency improves. However, practical and material limitations often restrict the temperature difference, as exceedingly high temperatures can damage engine components and safety becomes a concern. Therefore, while a larger temperature gradient can theoretically improve efficiency, real-world applications must balance this with material and safety considerations.

Future innovations in heat engine efficiency are likely to be influenced by advancements in material science, artificial intelligence, and nanotechnology. New materials that can withstand extreme conditions while maintaining integrity will allow engines to operate at higher efficiencies. Artificial intelligence and machine learning could optimize engine operation in real-time, reducing inefficiencies. Nanotechnology offers prospects of developing materials and coatings that reduce friction and wear, further enhancing efficiency. Collaboratively, these innovations aim to push the boundaries of current limitations, offering prospects of more efficient, sustainable, and reliable heat engines.

Materials used in heat engines are selected for their ability to withstand high temperatures, resist corrosion, and endure mechanical stresses. Alloys of steel, nickel, and titanium are common, owing to their high melting points and strength. In jet engines, for example, materials capable of withstanding high temperatures without losing strength, like Inconel, are used. These materials contribute to efficiency by allowing engines to operate at higher temperatures, where they can potentially convert a greater proportion of heat energy into mechanical work, thus, material engineering is a crucial aspect in the pursuit of heightened engine efficiency.

Heat engines cannot be 100% efficient due to inherent physical limitations and the second law of thermodynamics. Every real process involves some energy loss, often as waste heat dissipated into the surroundings. There's also energy lost due to friction, air resistance, and other mechanical inefficiencies. Additionally, materials used in engine construction have their limits and can't withstand indefinitely high temperatures or pressures. The second law of thermodynamics states that there will always be some energy that can't be converted into work, affirming the impossibility of 100% efficiency in any heat engine.