I need a GSM (European) thermometer that can send SMS messages with
temperature. Either automatically (e.g. once a day) or on demand (e.g. by SMS or
call).

I was only able to find many overly complex GSM modules for EUR 500+ that
one could use with an attached thermometer probe for $5 but I think
it's an overkill.

Is there anything simpler and at least a bit cheaper?

Hi,
just in case you didn't know:
Nokia has a gsm with a thermometer in it, it's quite cheap because it
is one of their basic models.

Dear cubist,

Thanks for the comment. I know about at least two Nokia phones that
have a thermometer built in. I read it doesn't measure ambient
temperature but temperature of the battery. It's not a big problem for
me because the battery temperature does have a correlation to ambient
temperature and might work well for what I need.

However, it is my understanding that if I leave the phone alone I
cannot read the value in any way (via SMS or call). One has to be
present to read it from the display of the phone. Correct me if I am
wrong and I will buy it!

Hi, can you attach the thermometer to a PC?  If that can be done, you
can create a simple program to read from a digital thermometer, than
SMS out using your mobile phone.

Here's a free SMS software that provides a commandline interface.

http://www.visualgsm.com