My suggestion for this is... you can better go for refrigeration (4 Deg C). For long term preservation, it would be better for maintaining those fungal cultures active upto 5-8 months.
It may depend on the broth/growth/culture media used(?), but perhaps you should have a short view/quick glance into:
www.condalab.com/pdf/1015.pdf :
"Time and temperature of incubation vary considerably according to the fungi. As a general rule, incubate for 1-2 weeks at room temperature (approximately 25°C). Most Penicillium grow best between 20 - 25°C; Aspergillus species grow well at around 30°C, but Aspergillus fumigatus grows well at 50°C and C. albicans at 25°C during 24 - 48 hours"
In HEIN et al, PNAS vol. 112 no. 42, October 20, 2015 , pp. 13039–13044, doi: 10.1073/pnas.1511197112 = http://www.pnas.org/content/112/42/13039.short in the supporting material=
http://www.pnas.org/content/suppl/2015/09/30/1511197112.DCSupplemental/pnas.201511197SI.pdfI found both fungi and a different storage of conidia after cultivation/culture of fungi.
For Aspergillus in General you should visit the Special website www.aspergillus.org.uk/ wher you perhaps will find valuable information about the matter you want to know.
cf. also as only one out of several articles:
Elias K. Manavathu, George J. Alangaden and Pranatharthi H. Chandrasekar:
'In-vitro isolation and antifungal susceptibility of amphotericin B- resistant mutants of Aspergillus fumigatus.'
Journal of Antimicrobial Chemotherapy (1998) 41, 615 –619 (see Methods section) @: http://jac.oxfordjournals.org/content/41/6/615.full.pdf
Additionally do a Google search for
| Storage of Candida albicans AND Aspergillus fumigatus culture plates Room temp* AND OR 4°C |
Perhaps this is of help anyway, best wishes and good luck!
In my opinion, keeping the plates in refrigerator is better. Addiotionally you can wrap the plates using laboratory films, such as parafilm, to prevent medium dryness.
For long-term storage, culture plates are not the best option, you can use liquid medium with glycerol added and store at -80°C.