Thank you for your comment, manikantants, but it doesn't work either with the absolute paths specified. Now, I have logged the crontab output during one run. These are the errors generated when calling the IDL routine in the script and running it from the crontab:

% Compiled module: PLOT_TEST.
% Compiled module: LOADCT.
Xlib: connection to ":0.0" refused by server
Xlib: No protocol specified

% WINDOW: Unable to connect to X Windows display: :0.0
% WINDOW: Unable to open X Windows display.
Is your DISPLAY environment variable set correctly?
% Error occurred at: LOADCT 106 /d/appl/rsi/idl64/lib/loadct.pro
% PLOT_DAY 8
/usr/people/.........../plot_test.pro
% $MAIN$
% Execution halted at: PLOT_TEST 8

Please, can anybody tell me which settings I should change?