Having said that, if a young Tomato seedling is subjected to very high temperatures (say 30C+) for any length of time it can easily die. This is why whenever I put mine into the plastic greenhouses I watch the weather very carefully, and often leave the flaps open.
Tomatoes that have been grown well are usually what I would call "stocky" - not too tall and not too thin - and will have fresh-looking dark-coloured leaves. This one looks OK:
If the leaves are very pale, or have a dull matt look, then the plant is probably not healthy, and may be suffering from mineral deficiency, something often associated with poor compost. [Google "chlorosis" for further info]. Lots of the mass-produced composts available these days are basically rubbish (literally), and contain very few nutrients, and those can be exhausted in a matter of days. This year I sowed my Tomatoes in John Innes No.1 mix, rather than multi-purpose compost, and I'm very happy with the result. This type of compost is formulated specifically for seed-sowing of for very young plants. When I re-pot my seedlings into bigger pots (soon!), I will use John Innes No.2 mix.
My Tomato seeds were sown this year on 24th March, and spent their first few days ensconced in plastic bags in the airing-cupboard. Once they germinated I transferred them to the Growlight House (which provides lots of light but very little extra heat), where they lived for about 10 days. By this time they were about two or three inches tall, and had their first pair of proper leaves. At this stage I began to give the plants as much natural daylight as possible, initially on a windowsill, but then in the little plastic greenhouses. (See my April Hokey Cokey post). The gradual acclimatisation to outdoor conditions is paying off, because the plants now look really good:
The seedlings are sturdy, and brightly-coloured. Just what I want.
The only trouble is, the weather has taken a definite turn for the worse, with a succession of dull, windy, cold days and night-time temperatures hovering around zero or just above. I have had to keep the Tomatoes (and their Chilli friends) indoors all the time, and they won't like that.
You will have noticed that my Tomatoes are at present in those Elmlea pots. I like these because they are tall and thin, which has two advantages: first, it allows the seedlings to produce long roots; and second, it allows me to squeeze more pots into the Growlight House! Before many days have passed, I will move the plants into bigger (5-inch / 13cm) pots, in which I will grow them on for another couple of (possibly 3 or 4 ) weeks until the weather improves enough for them to go into their final homes, which will be these 35cm (13.8 inch) square planters.
Having gradually built up my collection, I now have 12 of these big planters (officially called "balconnieres", made by Stewart), along with four more of a similar but not so ritzy design, so I am going to be able to grow 16 decent-sized Tomato plants this year. Whether I will be able to resist the temptation to grow some more in less suitable containers remains to be seen!