When I bought my tantrum (stock 502 MPI) the thermostat typically held at about 180. Last year it overheated (pump went out) so the pump was replaced and everything was cleaned out. This year the thermostat has been reading just below the buzzer at 240. I haven'd noticed anything wrong performance wise. Do you think this could be a thermostat problem or can my boat run normally at 230ish?

Oil temp stays below 180 (bottom of gauge)...

240 is bad if that is the real temp. Did you back flush the system to get the pieces of impeller that shredded out? Run it at 2000 rpm in neutral and see if you have good water coming out the the back, should be enough to fill a 3 gallon bucket in seconds

Boat should run right where the thermo is set or slightly higher (10 degrees) when u do wide open runs

Did you pull the pieces out at the oil cooler intake line. Thats where they will be.

All of the pieces were flushed out of the system and the temp was checked and found to be OK last year...

Do you have a water pressure gauge?
Have you verified with a laser temp gun?

I'll have the marina verify the temp this week. What is the normal water pressure reading?

The alarm should go off around 200-210*. The alarm temp sensor is separate from the gauge sensor. I doubt you are actually running as hot as the gauge shows. It could be a bad gauge or sensor.
230-240* is way hot and you would have all kinds of steam coming out the exhaust.

Great info. The gauge always shows the temp just below 240, but the buzzer never goes off, performance is not affected, and there is no steam. I'm going to remove the plugs (one at a time) and flush the system out tomorrow.

Before you do that,

1) Running on hose see how much water is coming out of your exhaust.
2) Get a real temp reading from your thermostat area using a temp gun.
3) Pull the feed hose off the transom assembly, just follow the sea water pump hose back. It should be an 11mm bolt make sure its not restricted.
4) keep in mind when your impeller went last year it may have worn the pump housing and now the pump can not make enough pressure.

Good Luck.