The original Arduino UNO programm is much longer, I brought this back to its bare minimum to show my problem. Sorry, I forgot to skip the include <SoftwareSerial.h>.
Unfortunately there is no information available how to communicate with the heating device. But others, including me, discovered a lot of details about this i.e. the communication is Serial, 9600 baud, 8 bit data, no parity, 1 stopbit; no end-of-line or whatoever. I found also how to generate the checkbit in a message and which start and stopbytes are required.
I can succesfully send data to the heating unit by means of the RealTerm software. I use its possibility to send a file. This file contains exact the same data as in int R1[] in my sketch. In this case succesfully means the heating unit accepts this data or several other files from the RealTerm programm and reacts as expected. It looks to me the Arduino sketch opens the serial communication in a peculiar way.