The conversion efficiency proposition for hydronic solar heating might be feasible.. ie solar water heating panels and a lot of thermal mass, probably just water tanks, stored inside. And a lot of insulation and really good air sealing too.
But like cadillackid says, heating has its greatest demand at times when there's the least energy available from a solar PV system. Rent would save a lot of money.
As for data: yes, I do have a little. A couple years ago I ran an overnight heat loss test in my bus. At the time it was very much stock; I hadn't removed any windows nor added any insulation. It's a transit style Blue Bird, 38 feet long. It was parked outdoors and had 5 kW of electric baseboard heater laid in the aisle on the floor in the middle of the bus. I wired the heater to be always on; there was no thermostat. As I recall the numbers, the outdoor temperature got as low as 14° F and the bus temperature, measured at just one point, was 54° F. I don't recall where I left the temperature sensor but I expect it was somewhat central in the bus, maybe 5-6 feet away from the heaters. The ends of the bus must surely have been colder.
Working with really rough numbers: 5 kW continuous all night long managed to hold about a 40° F temperature differential. Things warm up fairly quickly when the sun is out. If we say that energy draw was continuous from 7 pm to 7 am it's 12 hours: 60 kWh of energy to be collected on an array and stored in a battery every day. And not even all that comfortable as indoor temperatures go.
We won't say it's impossible, but most probably would say it's impractical. Deleting windows and adding insulation certainly will help.