Adding a capacitor at the radio solved my issues... Sorry for not trying that from the very beginning, today I bought some capacitors, and now it looks good!
Happy now!
33804 TSF:MSG:SEND,3-3-0-0,s=1,c=1,t=0,pt=7,l=5,sg=0,ft=0,st=OK:24.0
33818 TSF:MSG:SEND,3-3-0-0,s=2,c=1,t=1,pt=2,l=2,sg=0,ft=0,st=OK:62
34127 MCO:SLP:MS=60000,SMS=0,I1=255,M1=255,I2=255,M2=255
34134 MCO:SLP:TPD
34136 MCO:SLP:WUP=-1
Sending initial value
34154 TSF:MSG:SEND,3-3-0-0,s=1,c=1,t=0,pt=2,l=2,sg=0,ft=0,st=OK:1
Requesting initial value from controller
34164 TSF:MSG:SEND,3-3-0-0,s=1,c=2,t=2,pt=0,l=0,sg=0,ft=0,st=OK:
TempDiff :1.01
HumDiff :1.50
T: 23.00
H: 65