I cannot speak to heating but here is a list based on the TA ratings with proximity to INEC.

Killarney Lodge TA#2 on Countess Road off Muckross Road. Close to town and about a 15 minute walk to the INEC.

Elyod House TA#4 on Ross Road off Muckross Road. Close to Ross Castle and about 10 minutes walk to town and 20 minutes walk to INEC.

Robeen House TA#10 on Muckross Road. Only a few minutes walk from the INEC.

Shraheen House TA#13 on Ballycasheen Road (an extension of Woodlawn Road off Muckross Road. About a 20 minute walk to both town and INEC. A bit out of the way in my opinion.

Chelmsford House TA#15 on Muckross View off Countess Grove off Countess Road off Muckross Road. Less than 10 minutes to town on a quiet walk but over 20 minutes to INEC.

Abbey Lodge TA#17 on Muckross Road. 5 minutes directly into town and less than 15 to INEC.

The rest are either on Muckross Road or just off it.

Woodlawn House TA#20 on Woodlawan Road. Just a stone's throw off the Muckross Road, half way between town and the INEC.

Oaklawn House TA#27 on Muckross Drive (quiet area) just off Muckross Road. Again just off the Muckross road between town and INEC but closer to town.

Ardree House TA#29 on Muckross Road but much closer to town than INEC.

Rivermere Guesthouse TA#33 on Muckross Road about halfway between town and INEC.

There are many more B&B's on the Muckross Road but seem to have lower ratings on TA so I will stop here.

If you find something you think is interesting from elsewhere just let me know and I can tell you of its location with respect to town and the INEC. Unfortunately I have not stayed at any of the B&Bs and so can only recommend based on others experience.