Without seeing your models, it is difficult to give you a precise answer as to what you have. Being from New England and seeing a lot of BAR cars, I direct you to the "Northern New England Color Guide to Freight and Passenger Equipment" by David R. Sweetland and Stephen Horsley, by Morning Sun Books, ISBN 1-878887-36-4.
First of all, BAR did not roster any 40 foot mechanical reefers. BAR reefers were painted yellowish orange, not red, white and blue. All 40 foot reefers were ice cooled with roof hatches for filling the bunkers. Because of BAR's affiliation with Pacific Fruit Express, BAR owned cars built by Pacific Car and Foundry, using PFE specifications. The plug door cars numbered 7000-7856 were R40-26 clones while the swing door cars in the 8500-8574 and 8600-8749 series are square cornered R40-10s and R40-10 look-alikes. BAR 8575-8599 appear to be ex-PFE R40-14s. Intermountain-Railway Company occasionally has PFE R40-10 and -14 models available in HO. BAR also rostered ex-MDT cars similar but not exactly like the PC&F cars.
BAR also rostered some plug door XIH class 40 foot boxcars for newsprint and potato service. These cars did not have ice bunkers or roof hatches but did have underfloor heaters, and had ventilator control mechanisms high on the side near the ends. Cars 2000-2299 were built by Magor Car Co. while 2300-2449 were PC&F products. These dual purpose cars were the first BAR cars to wear the red, white and blue, State of Maine Products paint scheme BAR is famous for. Interestingly, the New Haven tacked an order for 100 cars onto the BAR's PC&F order and, it was cheaper to have them delivered in SOM paint instead of a totally new scheme.
As far as prototypical, your Train-Miniature car is closest but, it is definitley not exact, with incorrect ends, no vent mechanisms (available in HO from Moloco), ice hatches, and no heater. BAR had cars all over the place in number series but 3246 was not used on XIHs. Your other car--without knowing more, I doubt if it comes up to the prototypical accuracy of the Train-Miniature car.
The SOO Line had potato cars as well. Reefers, or insulated box cars with hinged doors, painted blue.
Picture from the "O gauge Railroading On-Line Forum".
The Waupaca Historical Society has one at the SOO Line depot in Waupaca, WI.
http://www.wamrltd.com/?action=mikeKirk
Scroll down to see the photo. They also host a VRF cam.
Mike.
My You Tube
Potatoes may have been shipped in reefers, but did not need to be cooled. However, when potatoes were shipped in cold weather, they did need to be kept warm enough that they wouldn't freeze. In the winter, in earlier times, they were often shipped in reefers, with charcoal burners in the ice bunkers, and in later times, in mechanical reefers, which could provide the needed heat.
Train Miniature cars are among my favourites, but all of their plugdoor cars which I had, also had ice hatches. This meant that they were ice reefers, equipped with ice bunkers which would have, in the winter, charcoal-burning heaters if they were moving potatoes.
Most of mine were painted for one of my freelanced roads, but the ice hatches are definitely visible...(click on the photos for a larger view)
Here in Canada, both the CPR and CNR used the charcoal heaters in the ice bunkers (when appropriate). Many of those cars had small exterior doors, allowing direct access to the bunker area.
Later, they developed reefers with overhead ice bunkers, and underslung self-feeding charcoal heaters, with the cars' inside-temperature automatically-controlled...This is an Athearn reefer, modified to represent one of those cars...
Wayne
I recently acquired two of these red, white, and blue reefers on ebay in seperate purchases. I'm not sure who manufactured the first one but the one that just arrived today is by Trains Minature. The first one had an all black roof and ice hatches. The second one was simply a plug door car with no ice hatches indicating to me it is a mechanical reefer. It also has a blue roof with a silver roofwalk. Here is the odd thing. Both are numbered 3246. The only way this would make sense is if the ice cooled reefers were converted to mechanical reefers and the second one is just a later iteration of the same car. Was that something that might have been done with the ice cooled reefers or is one of these cars non-prototypical?