I am not sure whether I understand the question that is being posed. If I understand correctly, you are stating that at startup the reactor contents cool as you increase the heating oil temperature. During startups the dynamics of a system can be quite different than during steady state operation. Depending on the initial temperatures of the hot oil system (vessels, piping plus oil inventory), reactor system (vessels, piping and inventory) and raw material conditions, there could be transients in which the reactor contents are heating the vessel faster than the oil system can heat the reactor contents. This would result in a decrease in reactor contents as you heat the oil system. The system must be analyzed on a transient basis during startup and shutdown in order to understand the time-temperature history of oil, process and equipment.
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