Is a multi-entry visa necessary if I've visited Thailand twice for one month each in the same calendar year?

there is no limit on the number of visa exempt entries

Not necessarily. Two visits of one month each only amount to a total of about 60 days in Thailand on visa exemption. Even with another 30 day visit you would still only be at around 90 days in total, which is normally well within what immigration considers ordinary tourism. Immigration tends to focus more on cumulative stays that start to resemble living in Thailand. A tourist visa can provide slightly additional predictability, but at that stage it is usually not strictly necessary.

Yes

If you did not get a warning from Immigration last time you entered that next time you need a visa you should be fine

Very broad question with too little background information. But if you want to enter thailand 2-3 times per year for one month, if you are from a qualifying country, you will be fine on visa exempt. If not, buy a regular TR tourist visa (single entry) each time around. Should each of your one months stays fall within a period of 6-8 months, you could also look into the METV, whoch would give you multiple entry in a 6 months timeframe.