Do they supervise your sample
Employment-related U/As are unobserved unless you had been suspected of tampering.

how strict are they on temp levels?
The acceptable temp range is 90-100F, as mandated by the DHHS.

Do you think my temp levels will be alright if i pick it up right before going to the testing lab.
A handwarmer pack will ensure that the temp will not drop out of range en route to the collection site. Handwarmer packs can be found at any camping/hunting/sporting goods store.