mine doing same thing.. may be a thermostat sticking??
It is the only thing i can come too.
The Waterpump seems to be running fine as when i grap the hoses after running for a while both sides are hot which tell me that it is flowing thru the RAD, thus the pump is running.
It has to be the Stat sticking from time to time and not opening it up.
The only part that is confusing is why do i have heat, then don't have heat and so on, so on.
I am changing the Stat tonight... Hopefully i have the right one as they only list it for a 2000 celica (doesn't even say GTS, GT or 1zz or 2zz) so i am just assuming the both blocks use the same stat. Will let ya know if that fixes my problem