There are a couple of options:
This is a small trickle charger that works for 12 volt starter / 12 volt auxiliary house batteries. It provides a small trickle charge.
It is temperature compensated so it deals with the need to slightly change the charging algorithm as the starter battery temp changes.
Prevent dead starter batteries in your RV. House2Start charges your engine battery automatically from the house battery.
house2start.com
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These newer red BTB chargers from Sterling have a built in reverse charge function.
Importantly - it only activates when the house battery voltage is high enough. The intention is to channel excess solar from the house battery to the starter battery.
There is also a manual way to use it in sort of a jump starter method.
battery to battery chargers, battery to battery charging. Charge a 12v battery from a 24v. Charge a 24v from 12v. on the run battery charger, on the water charger, marine DC to DC battery chargers, dc powered charger, mobile power supply, inverters, generators, professional mariner, piggyback...
www.sterling-power-usa.com
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There is a company that makes a dual output solar charge controller that will charge both the house and starter battery - but I cannot remember the name of it.
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The main challenge for a battery in the bed are the Li battery BMS limits. For nearly all of them, the minimum charge temperature ( for the core of the battery ) is ~ 30-35 F, at that point the BMS will block further charging. 'Usually but not always", the minimum discharge temperature is ~ 5 F, bot some trip both off at the same time.