Seniorvos:
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.
No, it opens it in a normal way, but as someone pointed out, it is TTL level; not RS232. Some RS232 devices will accept TTL level signals, but certainly not all of them
When you use RealTerm to communicate with it, are you using a USB->RS232 adapter? If so, it is likely to be RS232, and not TTL. You can use a MAX232 chip to generate true RS232 from 5V TTL serial.