We've rented an enormous kerosene heater to heat up the house so that the pipes would thaw. We've been at it for many hours now and no results. Don't want to leave the heater on all night obviously, but we're concerned giving up now means the pipes will freeze again. What can we do?

What do you mean by hydronic heating pipes? Do you mean a boiler and a hot water heating system? If so, are you sure that the problem is frozen pipes. I don't see how the pipes of a hot water heating system could freeze if the system is in operation and working.
I urge you to be careful using a kerosene space heater. Not only of the flame but also of the carbon monoxide which is the real danger. Should only be used in well ventilated areas.

Thanks for your response. We did some research on the kerosene heater, and yes, also have some concerns about the carbon monoxide. We are not in the same room as the kerosene heater, so there's less of that issue, but the greatest problem is that it's simply not working. It was on the recommendation of a plumber who suggested there was no other way to thaw the pipes. Hydronic heating systems are used in baseboard heating. The water pipes work fine, they are attached to a different boiler. We had turned off the heat entirely (my husband didn't realize this would be a problem) and found in the following morning that the heat wouldn't come back on. Another plumber tried pushing hot water from the water boiler into the pipes, but found that the water wouldn't make the circuit, and couldn't melt through the clog. He'd been trying for about 5 hours.

Carbon monoxide is sneaky stuff. Don't even be in the same house if you are using one of those "jet" heaters.