Certain Dangerous Goods require mandatory transport in reefer containers due to safety reasons. These are some of the Self-reactive Substances under Class 4.1 and some of the Organic Peroxides, Class 5.2. This requirement is listed in column 16 of DG List in chapter 3.2 and respective sub sections in chapter 2.4 & 2.5 of IMDG Code (35-10).
Let us look at the provisions of other dangerous goods which do not require refrigerated containers but are offered sometimes as temperature controlled.
So what goods which do not require a reefer is sometimes transported in reefer? Generally these are Perfumes ( UN 1266), Safety Matches ( UN 1944), Paint (UN 1263), Lithium Batteries (UN 3090,3091,3480,3481). Some shippers transport these in live reefers to maintain the product quality. Of course Calcium Hypochlorite require live reefers by most of the shipping lines due to its bad past.
IMDG Code has certain provisions for Dangerous Goods in reefers for commercial reasons, these are specifically related to Flammable Gases ( Class 2.1) and Flammable liquids ( Class 3). When Flammable liquids having flashpoint less than 23 °C c.c is transported in live reefer then
1/ Substance shall be precooled and
2/ Transported at a temperature at east 10 Deg C below its flashpoint
Or explosion proof reefer is required.
At any moment during transport In case the reefer fails then power supply shall be disconnected and must not be switched on again.
No line will accept flammable gas in live or non-live reefers. ( For full details refer 7.7 of IMDG Code)
IMDG Code Compliance Centre 
The storage power for a reefer container is calculated by the hour how is the treatment of a reefer container plugged out at 1:15am? Should the 15 minutes be rounded up to 30 mins or 1 hour?
Is there an international regulatory body that monitor and calibrate refrigerated containers?
Cathy, You may contact the ocean carrier for clarification.
Regards/Shashi
For reefer containers containing hazardous cargo, does the temperature have to be checked every six hours, while on board?
Yes, reefer need to be monitored at frequent intervals.
I need two explosion proof reefers in jersey city new jersey to store and keep cool drums of polymer grout for bridge project