I can always fire my heating up with no engine running even on a short days running and I only have 3x 90Ah batteries on domestic system, a good diesel heater shouldn't take too much to run once started.
If shorepower is fitted there should be a lead somewhere as long as you have lecy cards, often there is enough left on leccy posts so check before you load a card to it.
As said before start warm and you stay warm, a hot water bottle in a bed does wonders, I have heating outlets in my berth and spare ducting I run under the duvet and as long as I get into a warm bed I stay warm whatever the weather.
Stick with it, we all make the odd bad mooring even after 20 years and as long as nothing is badly damaged and no-one is injured it's good, as long as you are prepared to appologise to people it's generally not a big thing.(and if it's another hire boat they don't care either)