I will try 2 solutions: without solvant (if it safe in your case), or under pressure by doing it in closed vessel (like reactor for hydrogenation..), it easy by this way to increase temperature of solvant/reaction without boiling..
Since there are problems upon carrying out the reaction at 188 oC for 2 days, then my advice is to change the set of conditions (another lower temperature, a new exertion of pressure, possibility for usage of catalyst, closing the reaction vessel, stirring...).
Actually the most important thing is to check if your reagent will decompose at this temperature?! If this is not the case then you may run the reaction inside autoclaves (if you expect to have a pressure higher than 6 bar) or inside fisher porter bottles (if you expect to have a pressure lower than 6 bar).
There are specialized heavy walled glass tubes (Carius tubes) designed for the purpose. You should be sure no gas is generated in your process - and in all cases, heat the tube behind a shield (and freeze with dry ice before opening.) For scales larger than a gram or so, an autoclave is best, although not all labs have such equipment.
Why should you run the reaction for two days at 188°C, with lower boiling points solvent and reagent? And how to run your reaction at 188°C with lower BP solvent and reagent ? under reflux? or pressured reactor?
If You have run your reaction for two days under reflux at 188°C with acceptable result, then you may chang your solvent with higher BP sovent that may help you to raise your reaction temperature with resonable shorten reaction time. However, If the boiling point of your reagent is very lower than the reaction temperature188°C. I suggest you try to run your reaction with pressured vessel directly, which may improve your reaction result even at lower temperture.
If reaction condition which described above was under pressured condition. It is almost no way to improve your reaction rate at lower or the same temperature through tuning for other reaction parameter. You have to try to change your reaction system design. In other word, you needed to find out your new catalyst to reduce the activation energy and enhance the reaction rate at lower reaction temperature.
The temperature of the solvent inside the flask will be the reaction temperature & not outside temperature . So change the internal solvent having required higher B.P.
1. Change solvent and bring in the one with high boiling point. Even then ,you will have to ensure that the bubble point (which is different from boiling point) of the system(solvent plus reagent) is higher than 188 C required by you over the entire range of reagent concentration handled in your reaction.
2.If for any chemical path convenience etc, you are constrained to use the solvent you are using now, change (increase) the operating pressure in your reactor. This you can know from vapor pressure - temperature chart for your solvent.