How much does silicone oil expand by when heated?

The general ‘rule of thumb’ for silicone oil is that it expands (or contracts) by approximately 10% per 100°C (1% per 10°C).  Note that this relationship can vary depending on the temperature and the particular thermal fluid used.  (The datasheet of your thermal fluid might contain some relevant information.)

When estimating the expansion of oil with heating, you need to be consider the oil in the Huber unit, in the hoses and in the application (e.g. vessel jacket).