I've stopped thinning our carrots as it's such a fiddly job. Just sow them as thinly as possible by hand and harvest them by the fork full, discarding the little ones. The seeds are very cheap and we had a great result last year using that method. Doesn't work for beetroot or leeks though.
For fine seeds mix an eggcup of dry wood ash & some dry silver sand add the seeds by sprinkling them over the material when it's laid out on a sheet of paper , put it back in the egg cup and thinly sow a pinch at a time along a cord line row If you are able two long strips of planed wood or plastic can be laid a penil thickness apart alongthe string . do your sowing as best as you can between the strip then tip each strip up to drop any seed on it into the drill .
Carrots do best when the soil temp hits 20 oC or better
Now laugh at what I do ,I made some sowing masks .
I got hold of some 2 mm thick plastic sheet . made accurate 13 " squares of it then marked & cut 1/2 " holes in it with a cheap Chinese eBay diamond hole cutter using my bench drill so I have mask patterns of sowing squares with 16 , 12 , 9 & 5 holes in them . As three are no rough edges to the holes it so easy to lay a mask on my 900 mm high raised beds and pop a few seeds on th material then use a finger tip to slide a single seed in a hole ( keep to a rigid sequence so you only put one seed in each hole . When done sieve very fine dry soil over the mask and press it in the holes . Remove the mask and lightly fine sprinkle water over the sown square.
Last year for the two of us I did 3 beds of 9 square feet with 16 carrots per square foot carrots spaced at 3 "apart in all directions .
I cleared the beds a fortnight ago and pressure canned 24 pints of carrots that will see us through until the early carrots are here and on till the end of march 2022.
I've all so sown loads of other seeds using masks to have them thinned from the start ( All our four beds of onion sets are sown accurately using a mask on the bed too .. the four inch spacings makes weeding & feeding them so easy . This year we have three beds of brown onions and one bed of shallots which should give us about 350 onions to harvest & store for use in late August 2021 through to end of May 2022.
I've resorted to this level of precise calculating requirements & sowing so we can plan ahead what crops we can have and adjust our diets accordingly . It works well .. I've also drawn up an accurate sowing planting out & harvesting calendar which brings things into a much better perspective for continuous cropping and no waste .
Meaning we can also use the same packet of seeds stored cool & dry over three or so years .