Thanks. I tried the F() - macro and deleted some of the debug message lines. Code size increased slightly.
I added
char webpath[] PROGMEM = "/Temperatures/connect.php";
and changed the function httprequest to :
char srequest[128] = {0}; // zusammengebastelter Request
char string_temp[4][8] = {"0.0","0.0","0.0","0.0"};
Serial.print("sending request :");
dtostrf(akttempsC[0], 4, 1, string_temp[0]);
if (akttempsC[1] != -50.0) dtostrf(akttempsC[1], 4, 1, string_temp[1]);
if (akttempsC[2] != -50.0) dtostrf(akttempsC[2], 4, 1, string_temp[2]);
if (akttempsC[2] != -50.0) dtostrf(akttempsC[3], 4, 1, string_temp[3]);
// Normalen Request an den Server senden
sprintf(srequest, "?a=%d&t1=%s&t2=%s&t3=%s&t4=%s&r=%d",
settings.anl_no, &string_temp[0], &string_temp[1],
&string_temp[2], &string_temp[3], relaisstate);
Serial.print(F("params :"));
Serial.println(srequest);
ether.browseUrl(webpath,srequest, website, response_callback);
Now I see debug lines on every request that should be sent to the webserver.
...
sending request :params :?a=1&t1=-50.0&t2=0.0&t3=0.0&t4=0.0&r=0
...
But the data does not seem to pass its way to the webserver. No lines in the apache log and the tcpdump lines state a length of 0 
20:46:01.174719 IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 44)
192.168.100.36.2896 > rover.hoover.home.http: Flags [S], cksum 0xef9d (correct), seq 21504, win 768, options [mss 550], length 0
Any ideas, what I'm doing wrong here? Thanks in advance.
Harry