What's the volume of the loop, the time to record 1°C of rise, where is temperature being measured, how accurate is the measurement device, what temperature is the loop normally cooled to, what is the loop connected to such as heat exchangers, what is the ambient temperature of where the loop is situated, is the chiller operating correctly and actively cooling this loop, is the chiller sized correctly, are the pipes insulated, does any of the pipe pass through warm areas such as sunlight or areas of the facility where heat is generated?
Lots of factors that are a total mystery to anyone that would even begin to try and answer your question. I'm sure I could come up with several more.
Are you saying that your loop is generating more heat than can be removed by the chiller? And you're saying the pump is the only item adding heat to the system?