A battery cover assembly having integrated battery condition monitoring for measuring electrical current passing to and from a battery post, including an electrically conductive collar for connecting to a post of a battery, and an electrically conductive terminal for receiving a connector of a load. An electrically conductive resistor having a known resistance extends between outer surfaces of the collar and the terminal. The battery cover assembly is incorporated into a battery, which may also include a voltage measuring device connected between the outer surfaces of the collar and the terminal for measuring the voltage drop across the resistor, memory for storing the known resistance of the resistor, and a digital processor programmed to receive the measured voltage drop from the voltage measuring device, retrieve the known resistance from the memory, and calculate current flow through the resistor based on the measured voltage drop and the known resistance, whereby current flow to and from the battery can be measured. A temperature measuring device may also be incorporated to measure temperature of the resistor located between the outer surfaces of the collar and the terminal. A resistance-temperature table may be stored in the memory and used to calculate the actual resistance of the resistor and then to compensate the current value from the voltage measured across the resistor.