There are many rites that mark the beginning of winter in Rhode Island. There’s the first frost. The first snowflake. The first day when the furnace roars to life.

Oops, that last part isn’t for everybody.

For hundreds, perhaps thousands, of Rhode Island families, the house or the apartment stays cold at the advent of the heating season. That’s because they’ve fallen so far behind on their utility bills during the spring and summer that their gas or electric service has been shut off.

So every fall, Rhode Island experiences the perennial embarrassment of debating whether every home will have heat during the coming winter.

The question is always the same: How to get gas and electric service restored?

Once the juice is on or gas flows, a state-mandated moratorium limits most shutoffs between November 1 and April 15. It’s a quirk of the law that for the moratorium to take effect, the heat has to be on.

Some years, money has been raised to help households make minimum down payments on back bills.

This year’s strategy is a novel, if somewhat audacious, approach: simply asking the state’s now super-utility, National Grid (which since August controls most electricity and natural gas) to turn on every home on while repayment plans are worked out.

The “amnesty” proposal was the centerpiece of two weeks of noisy noontime demonstrations held outside National Grid’s downtown Providence offices, in the run-up to this week’s election.

And it was pushed in a letter to National Grid, sponsored by state Representative Arthur Handy (D-Cranston), and signed by 39 other legislators, including House Speaker William J. Murphy and Senate President Joseph A. Montalbano. GOP candidate Bill Harsch endorsed the universal turn-on. In an e-mail, Patrick Lynch’s spokesman, Mike Healey, writes, “The attorney general is committed to the idea of some sort of amnesty proposal, but he hasn’t seen any specific proposal to evaluate yet, and he knows that there’s no easy solution.”

So far, National Grid hasn’t warmed to the idea, says spokesman David Graves. One reason, Graves says, is that the proposal is too vague. For example: would there be income guidelines?

Graves notes that National Grid supports a complex energy law approved last summer, which could help low-income households through reduced utility rates and forgiveness of a portion of back bills.

That plan won’t take effect until mid-2007. In the meantime, there is a provision to allow some extremely poor households to make low down payments of 18 percent of their back bills, if they agree to pay full-freight on monthly bills.

Henry Shelton, the long-time advocate for the poor, says the new legislation may help, but that many homes still lack heat.

Just how many is always a question.

State Public Utilities Commission figures indicate that since the end of last winter’s moratorium in April and through September, 20,648 residential customers were shut off — and 12,406 had been restored, leaving a possible shutoff balance of 8242.

It’s not clear how many have restarted service, perhaps under new names, or who may be using space heaters or other potentially unsafe heat sources, or who are stone cold.