I have 3 x 35cm heated propagators, no thermostat. The thing is not to get seeds to germinate, but to look after them afterwards. I put a thermometer in one of mine out of curiosity, it was 26° in the propagator on the kitchen windowsill, another thermometer on the sill said 17°, so it was plenty warm enough to make the seeds germinate, which they have. But they will grow and then they'll need potting on and all that before it's frost free outside. Have you plenty of window sills, or, better still a greenhouse that's frost free? The baby plants would prefer it over 8 - 10° at night.
I have a greenhouse, but only a rather small feeble heater, too expensive to keep properly warm. I am transferring the babies to window sills, but there is a risk they'll get leggy reaching for light. Then they'll go in the greenhouse.
Zinnias like warmth, I'd wait a bit, then sow them in the propagator. Nasturtiums grow quite quickly and you can sow straight into the ground from late March to May. Cornflowers the same, they are hardy annuals. Lettuces too, they don't like it too warm. Peas shouldn't need a propagator either, they can go straight in the ground in March/April. As you've sown some they'll need getting out as soon as they've germinated, none of those plants needs to be very warm, but it's too soon for outside, who knows what the weather will bring!
A propagator is really good for half hardy annuals and tomatoes. I have sown lobelia, petunias, gazanias, verbena and rudbeckia Tiger Eye so far. They are the sort of plants that can't survive cold nights yet.
March is really a less risky time of year to sow.