PROVIDENCE, R.I. (AP) _ Free toasters are history. Today's banks offer thrills, excitement and chance to prospective depositors.

Support your favorite baseball team. Take a chance on the weather. Help an environmental cause. These are among the gimmicks banks are using to lure new accounts.

Fleet National Bank, based in Providence, has offered certificates of deposit that encourage customers to ''put your money where your mouth is'' by investing in a CD with an interest rate that increases each time either the Red Sox or Yankees win.

A New Hampshire bank offers a CD with an interest rate that varies with the daily temerature.

''From a competitors point of view, it's easier just to hike a rate,'' said Tom Howe, Fleet's senior vice president in products and services.

But the ''more creative type of deposit strategy - one that generates more enthusiasm and interest,'' helps broadens the market by targeting unconventional CD depositors, he said.

The method appears to work. Fleet has offered sports CDs since 1986, when the Boston Celtics were seeking their 16th NBA championship.

''We've been quite pleased with the results,'' said Howe.

The trick was to guess the number of points the Celtics would score in the final game. Those who guessed correctly saw their CD jump to 16 percent from 7 percent for the full three-month term.

When Providence College took on the University of Rhode Island at basketball in 1987, the bank capitalized on a long-standing feud by offering a CD with an interest rate that increased one-twentieth of 1 percent for every game the customer's chosen team won.

Fleet continued the sports tradition with a ''Home Team'' CD offered last fall in which the interest rate rose each time the Boston Bruins or Boston Celtics won a home game.

This year Fleet reoffered a baseball CD geared to the Yankees-Red Sox rivalry. Only available before the teams met for the first time June 8, the CD increases one-tenth of 1 percent from then on each time the customer's chosen team wins.

If the chosen team wins the American League Championship, the CD would receive a 1 percent bonus on the total deposit.

The Rhode Island State Police, responsible for enforcing the state's anti- gambling laws, say they have investigated the sports CDs and determined they are legal.

''You are really not gambling,'' said Sgt. Terrance Burgess of internal affairs. 'They are gong to give out a flat CD rate anyway so the element of chance, if it's there, is almost non-existent. You can't lose.''

The baseball CD required a $1,000 minimum deposit and offered a fixed rate of 9 1/4 percent for a six-month deposit.

Howe would not say how many sports CDs have been taken out.

''I think the fact that the bank has offered multiple sports CDs suggests that they are well recieved by the Rhode Island public,'' he said.

Rhode Islanders aren't the only ones who have welcomed the innovation. Lincoln Savings Bank in New York, for example, offered a similar CD based on the Yankees and Mets.

New Hampshire's Cheshire County Savings Bank offered a ''Heat Wave'' CD so unusual it took more than a month to catch on.

The interest rate on the three-month CD is 10 percent of whatever the day's high is in Concord, N.H. After October, the rates will be based on the temperature in Orlando, Fla.

If the temperature is a record high for the day, the CD would increase a half a percent more, said Elizabeth Colby, a customer service representative at Cheshire. The rate is guaranteed not to drop below 7.5 percent and has peaked at 9.75 percent since it began July 11.

''It took a little while for people to see what it's all about,'' she said. ''It's picking up.''

The CD, which requires a $500 minimum deposit, appeals to young people, partly because of the low investment and also because of the unusual terms, she said.

''Older people are more apt to want a fixed interest rate,'' said Colby. ''Younger people tend to gamble a little more.''

Fleet targeted another market with a CD it offered in the aftermath of an oil spill off the coast of Newport, R.I., earlier this summer, agreeing to donate to Save the Bay $1 per $1,000 deposited up to a maximum of $50,000.

''The oil spill in the bay obviously increased the awareness of most Rhode Islanders to the environment,'' said Howe. ''So we felt the timing of this product was really good.''

End adv for Monday Aug. 21.