Yes, a fluid with a lower temperature can still transfer heat to another fluid. The rate of heat transfer depends on various factors, including the temperature difference, the heat capacity coefficient, and the flow characteristics of the fluids involved.
In the scenario you described, where there is a cross-flow between air and water, it is possible for the water, even with a lower temperature, to transfer heat to the air. The heat transfer between the fluids is driven by the temperature difference between them. Heat will flow from the fluid with a higher temperature (in this case, the water) to the fluid with a lower temperature (the air) until an equilibrium is reached.
The heat capacity coefficient, also known as specific heat capacity, is a measure of the amount of heat energy required to raise the temperature of a substance. In your example, if the water has a heat capacity coefficient that is four times larger than the air, it means that the water can absorb more heat energy per unit mass compared to the air.
Even though the water may have a lower temperature than the air, its higher heat capacity coefficient allows it to transfer a significant amount of heat energy to the air. This can result in an increase in the air temperature, even if the water temperature remains lower.
It's important to note that other factors, such as the flow rate, surface area, and the heat transfer coefficient between the fluids, will also affect the overall heat transfer rate in a cross-flow configuration.