An integrated CRRT method and apparatus incorporates steps and means for compensating for heat loss from blood in an extracorporeal circuit. A blood warmer is designed to engage and hold a disposable blood tube segment to transfer heat at a closely controlled temperature to blood flowing in the disposable blood tube segment. Another significant aspect of the present invention is a blood tube segment for engagement with the blood warmer is located in downstream of a dialyzer and upstream of a venous pressure monitor, an air bubble detector and a venous line clamp. The disposable blood tube segment may be selectively connected when heat loss compensation is required and left disconnected when heat loss compensation is not required.