We may end up accepting both. Hot seems to be more common, but there are plenty hits for "not too warm".
But at least in Czech I would use them, although not strictly, in different contexts:
"Nebylo příliš teplo." When it was in fact quite cold.
"Nebylo příliš horko." When it was in reasonably warm but simply not overly hot.
The course generally seems not to accept "this morning" in sentences like this. I’m speculating here, but it seems to me that “in the morning” is less restrictive than “this morning.” “This morning” can refer only to today, while “in the morning” could also appear in a sentence like “It was not too warm in the morning on Wednesday.” Possibly dnes ráno would be used in referring specifically to "this morning."
I don't understand why the construction "The morning wasn't too warm" is not accepted. If anything it's closer to the Czech construction. There is no "it" to translate. Same for "Včera bylo dost chladno." in this section... Yesterday was quite cold is perfectly acceptable English, and closer to the Czech wording, yet isn't accepted. The required answer is It was quite cold yesterday - which again, as a construction, is further from the Czech as far as I can see.