I have grown chillies in an out house a few times and always get a good crop, but prone to pest. They love the outdoors here in the south. I grew spanish peppers and chillies outside last year, no problems whatsoever.
My toms have been in pots outside in the garden for 3-4 weeks, even had some mild frost early on but they were properly hardened of so it did not touch them.
My sweetcorn are about 2-3" in toilet rolls, then planted out deep. They grow roots from their stems like toms so can be buried without fear. Also helps with stability. I sowed them at the beginning of May.
I suppose I am risking frost but my instinct says go for it
